General
Easy
Physics-

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

Physics-General

    Answer:The correct answer is: The v minus x equation from the given graph can be written as,
    v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses
    therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v
    Substituting v from Eq. (i), we get
    a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets
    blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction
    Thus, a minus x graph is a straight line with positive slope and negative intercept.

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    Related Questions to study

    General
    physics-

    The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

    Slope of displacement time-graph is velocity
    fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3

    The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

    physics-General
    Slope of displacement time-graph is velocity
    fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3
    General
    maths-

    The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

    The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

    maths-General
    General
    physics-

    The graph between the displacement x and t for a particle moving in a straight line is shown in figure. During the interval O A comma A B comma B C and C D comma the acceleration of the particle is

    O A comma blank A B comma blank B C, C D

    Region O A shows that graph bending toward time axis i. e. acceleration is negative.
    Region A B shows that graph is parallel to time axis i. e. blankvelocity is zero. Hence acceleration is zero.
    Region B C shows that graph is bending towards displacement axis i. e. acceleration is positive.
    Region C D blankshows that graph having constant slope i. e. velocity is constant. Hence acceleration is zero

    The graph between the displacement x and t for a particle moving in a straight line is shown in figure. During the interval O A comma A B comma B C and C D comma the acceleration of the particle is

    O A comma blank A B comma blank B C, C D

    physics-General
    Region O A shows that graph bending toward time axis i. e. acceleration is negative.
    Region A B shows that graph is parallel to time axis i. e. blankvelocity is zero. Hence acceleration is zero.
    Region B C shows that graph is bending towards displacement axis i. e. acceleration is positive.
    Region C D blankshows that graph having constant slope i. e. velocity is constant. Hence acceleration is zero
    General
    maths-

    Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

    Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

    maths-General
    General
    physics-

    What is the equivalent resistance between A blank a n d blank B in the given circuit?

    R subscript 1 end subscript and R subscript 2 end subscript are in series
    therefore blank R subscript 12 end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals 4 capital omega

    R subscript 12 end subscript a n d R subscript 3 end subscript are in parallel
    R subscript 123 end subscript equals fraction numerator R subscript 3 end subscript cross times R subscript 12 end subscript over denominator R subscript 3 end subscript plus R subscript 12 end subscript end fraction
    equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction
    equals 2 capital omega
    R subscript 123 end subscriptand R subscript 4 end subscript are in series
    therefore blank R subscript 1234 end subscript equals R subscript 123 end subscript plus R subscript 4 end subscript
    equals 2 capital omega plus 2 capital omega
    equals 4 capital omega
    R subscript 1234 end subscript and R subscript 5 end subscript are in parallel
    therefore R subscript 12345 end subscript equals 2 capital omega
    R subscript 12345 end subscript and R subscript 6 end subscript are in series
    2 capital omega plus 2 capital omega equals 4 capital omega
    equals R subscript 123456 end subscript
    Now, R subscript 123456 end subscriptand R subscript 7 end subscriptare in parallel
    therefore R subscript c o m b end subscript equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction
    equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction capital omega

    What is the equivalent resistance between A blank a n d blank B in the given circuit?

    physics-General
    R subscript 1 end subscript and R subscript 2 end subscript are in series
    therefore blank R subscript 12 end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals 4 capital omega

    R subscript 12 end subscript a n d R subscript 3 end subscript are in parallel
    R subscript 123 end subscript equals fraction numerator R subscript 3 end subscript cross times R subscript 12 end subscript over denominator R subscript 3 end subscript plus R subscript 12 end subscript end fraction
    equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction
    equals 2 capital omega
    R subscript 123 end subscriptand R subscript 4 end subscript are in series
    therefore blank R subscript 1234 end subscript equals R subscript 123 end subscript plus R subscript 4 end subscript
    equals 2 capital omega plus 2 capital omega
    equals 4 capital omega
    R subscript 1234 end subscript and R subscript 5 end subscript are in parallel
    therefore R subscript 12345 end subscript equals 2 capital omega
    R subscript 12345 end subscript and R subscript 6 end subscript are in series
    2 capital omega plus 2 capital omega equals 4 capital omega
    equals R subscript 123456 end subscript
    Now, R subscript 123456 end subscriptand R subscript 7 end subscriptare in parallel
    therefore R subscript c o m b end subscript equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction
    equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction capital omega
    General
    physics-

    The current in the 1capital omega resistor shown in the circuit is

    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A

    The current in the 1capital omega resistor shown in the circuit is

    physics-General
    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A
    General
    physics-

    The current in the 1capital omega resistor shown in the circuit is

    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A

    The current in the 1capital omega resistor shown in the circuit is

    physics-General
    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A
    General
    physics-

    The total current supplied to the given circuit by the battery is

    The equivalent circuit of the given circuit is as shown

    Resistances 6capital omega and 2capital omega are in parallel
    therefore blank R to the power of ´ end exponent equals fraction numerator 6 cross times 2 over denominator 6 plus 2 end fraction equals fraction numerator 3 over denominator 2 end fraction capital omega
    Resistances fraction numerator 3 over denominator 2 end fraction capital omega blank a n d blank 1.5 capital omega blank a r e blank i n blank s e r i e s
    therefore blank R to the power of ´ ´ end exponent equals fraction numerator 3 over denominator 2 end fraction plus 1.5 equals 3 capital omega blank
    Resistances 3capital omega and 3capital omega are in parallel
    therefore blank R equals fraction numerator 3 cross times 3 over denominator 3 plus 3 end fraction equals fraction numerator 3 over denominator 2 end fraction
    The current, I equals fraction numerator V over denominator R end fraction
    equals fraction numerator 9 over denominator 3 divided by 2 end fraction equals 6 A

    The total current supplied to the given circuit by the battery is

    physics-General
    The equivalent circuit of the given circuit is as shown

    Resistances 6capital omega and 2capital omega are in parallel
    therefore blank R to the power of ´ end exponent equals fraction numerator 6 cross times 2 over denominator 6 plus 2 end fraction equals fraction numerator 3 over denominator 2 end fraction capital omega
    Resistances fraction numerator 3 over denominator 2 end fraction capital omega blank a n d blank 1.5 capital omega blank a r e blank i n blank s e r i e s
    therefore blank R to the power of ´ ´ end exponent equals fraction numerator 3 over denominator 2 end fraction plus 1.5 equals 3 capital omega blank
    Resistances 3capital omega and 3capital omega are in parallel
    therefore blank R equals fraction numerator 3 cross times 3 over denominator 3 plus 3 end fraction equals fraction numerator 3 over denominator 2 end fraction
    The current, I equals fraction numerator V over denominator R end fraction
    equals fraction numerator 9 over denominator 3 divided by 2 end fraction equals 6 A
    General
    physics-

    A current of 2A flows in an electric circuit as shown in figure. The potential differenceleft parenthesis V subscript R end subscript minus V subscript S end subscript right parenthesis, in volts( V subscript R end subscript minus V subscript S end subscript are potentials at R and S respectively) is

    Current through each arm
    PRQ and PSQ=1A
    V subscript p end subscript minus V subscript R end subscript equals 3 v
    V subscript p end subscript minus V subscript s end subscript equals 7 V
    From Eqs. (i) and (ii), we get
    V subscript R end subscript minus V subscript s end subscript equals plus 4 V

    A current of 2A flows in an electric circuit as shown in figure. The potential differenceleft parenthesis V subscript R end subscript minus V subscript S end subscript right parenthesis, in volts( V subscript R end subscript minus V subscript S end subscript are potentials at R and S respectively) is

    physics-General
    Current through each arm
    PRQ and PSQ=1A
    V subscript p end subscript minus V subscript R end subscript equals 3 v
    V subscript p end subscript minus V subscript s end subscript equals 7 V
    From Eqs. (i) and (ii), we get
    V subscript R end subscript minus V subscript s end subscript equals plus 4 V
    General
    physics-

    A 3 V battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be

    Resistance in the arms AC and BC are in series,

    ∴ R’=3+3=6capital omega
    Now, R’ and 3capital omega are in parallel,
    therefore blank R subscript e q end subscript equals fraction numerator 6 cross times 3 over denominator 6 plus 3 end fraction equals 2 capital omega
    Now, V=IR
    ⟹ I equals fraction numerator 3 over denominator 2 end fraction equals 1.5 A

    A 3 V battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be

    physics-General
    Resistance in the arms AC and BC are in series,

    ∴ R’=3+3=6capital omega
    Now, R’ and 3capital omega are in parallel,
    therefore blank R subscript e q end subscript equals fraction numerator 6 cross times 3 over denominator 6 plus 3 end fraction equals 2 capital omega
    Now, V=IR
    ⟹ I equals fraction numerator 3 over denominator 2 end fraction equals 1.5 A
    General
    physics-

    The equivalent resistance between the points A and B will be (each resistance is
    15 capital omega)

    The circuit can be shown as given below

    The equivalent resistance between D and C.
    R subscript D C end subscript equals fraction numerator 15 cross times open parentheses 15 plus 15 close parentheses over denominator 15 plus open parentheses 15 plus 15 close parentheses end fraction
    equals fraction numerator 15 cross times 30 over denominator 15 plus 30 end fraction
    equals fraction numerator 15 cross times 30 over denominator 45 end fraction equals 10 capital omega
    Now, between A and B, the resistance of upper part ADCB,
    R subscript 1 end subscript equals 15 plus 10 plus 15 equals 40 capital omega
    Between A and B, the resistance of middle part AOB
    R subscript 2 end subscript equals 15 plus 15 equals 30 capital omega
    Therefore, equivalent resistance between A and B
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction
    equals fraction numerator 1 over denominator 40 end fraction plus fraction numerator 1 over denominator 30 end fraction plus fraction numerator 1 over denominator 15 end fraction
    equals fraction numerator 3 plus 4 plus 8 over denominator 120 end fraction
    equals fraction numerator 15 over denominator 120 end fraction
    ⟹ R to the power of ´ end exponent equals fraction numerator 120 over denominator 15 end fraction equals 8 capital omega

    The equivalent resistance between the points A and B will be (each resistance is
    15 capital omega)

    physics-General
    The circuit can be shown as given below

    The equivalent resistance between D and C.
    R subscript D C end subscript equals fraction numerator 15 cross times open parentheses 15 plus 15 close parentheses over denominator 15 plus open parentheses 15 plus 15 close parentheses end fraction
    equals fraction numerator 15 cross times 30 over denominator 15 plus 30 end fraction
    equals fraction numerator 15 cross times 30 over denominator 45 end fraction equals 10 capital omega
    Now, between A and B, the resistance of upper part ADCB,
    R subscript 1 end subscript equals 15 plus 10 plus 15 equals 40 capital omega
    Between A and B, the resistance of middle part AOB
    R subscript 2 end subscript equals 15 plus 15 equals 30 capital omega
    Therefore, equivalent resistance between A and B
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction
    equals fraction numerator 1 over denominator 40 end fraction plus fraction numerator 1 over denominator 30 end fraction plus fraction numerator 1 over denominator 15 end fraction
    equals fraction numerator 3 plus 4 plus 8 over denominator 120 end fraction
    equals fraction numerator 15 over denominator 120 end fraction
    ⟹ R to the power of ´ end exponent equals fraction numerator 120 over denominator 15 end fraction equals 8 capital omega
    General
    physics-

    There resistances of 4blank capital omega each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between points A and D will be

    The equivalent circuit is given by

    4capital omega and 2capital omega resistances are in series on both sides.
    therefore 4 capital omega plus 2 capital omega equals 6 capital omega
    Then 6capital omega and6capital omega resistances are in parallel on both sides
    fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
    R=3capital omega

    There resistances of 4blank capital omega each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between points A and D will be

    physics-General
    The equivalent circuit is given by

    4capital omega and 2capital omega resistances are in series on both sides.
    therefore 4 capital omega plus 2 capital omega equals 6 capital omega
    Then 6capital omega and6capital omega resistances are in parallel on both sides
    fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
    R=3capital omega
    General
    physics-

    A particle starts from rest at t equals 0 and moves in a straight line with an acceleration as shown below. The velocity of the particle at t equals 3 s blankis

    Velocity of graph equals Area ofblank a-t graph
    equals open parentheses 4 cross times 1.5 close parentheses minus open parentheses 2 cross times 1 close parentheses equals 4 m divided by s

    A particle starts from rest at t equals 0 and moves in a straight line with an acceleration as shown below. The velocity of the particle at t equals 3 s blankis

    physics-General
    Velocity of graph equals Area ofblank a-t graph
    equals open parentheses 4 cross times 1.5 close parentheses minus open parentheses 2 cross times 1 close parentheses equals 4 m divided by s
    General
    maths-

    Period of sin space open parentheses e to the power of text sont  end text end exponent plus e to the power of text cur  end text end exponent close parentheses is

    Period of sin space open parentheses e to the power of text sont  end text end exponent plus e to the power of text cur  end text end exponent close parentheses is

    maths-General
    General
    maths-

    Period of fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction

    Period of fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction

    maths-General