Physics-
General
Easy

Question

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

  1. 2 blank m s to the power of negative 1 end exponent    
  2. 4 blank m s to the power of negative 1 end exponent    
  3. 6 blank m s to the power of negative 1 end exponent    
  4. 8 blank m s to the power of negative 1 end exponent    

The correct answer is: 4 blank m s to the power of negative 1 end exponent


    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

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    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

    L e t space f left parenthesis x right parenthesis equals fraction numerator sin left parenthesis x plus a right parenthesis over denominator cos space x end fraction
P r o p e r t y space o f space p e r o d i c space f u n c t i o n space o f space p e r i o d space space T
f space left parenthesis x plus T right parenthesis equals f left parenthesis x right parenthesis
B y space p u t t i n g comma space T space equals space straight pi comma space we space get colon
fraction numerator sin space left parenthesis straight pi plus straight x plus straight a right parenthesis over denominator cos space left parenthesis straight pi plus straight x right parenthesis end fraction
equals fraction numerator negative space sin left parenthesis x plus a right parenthesis over denominator negative space cos space x end fraction
equals fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction
equals f left parenthesis x right parenthesis
S o comma space t h e space p e r i o d space o f space f left parenthesis x right parenthesis space i s space straight pi.

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

    Maths-General
    L e t space f left parenthesis x right parenthesis equals fraction numerator sin left parenthesis x plus a right parenthesis over denominator cos space x end fraction
P r o p e r t y space o f space p e r o d i c space f u n c t i o n space o f space p e r i o d space space T
f space left parenthesis x plus T right parenthesis equals f left parenthesis x right parenthesis
B y space p u t t i n g comma space T space equals space straight pi comma space we space get colon
fraction numerator sin space left parenthesis straight pi plus straight x plus straight a right parenthesis over denominator cos space left parenthesis straight pi plus straight x right parenthesis end fraction
equals fraction numerator negative space sin left parenthesis x plus a right parenthesis over denominator negative space cos space x end fraction
equals fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction
equals f left parenthesis x right parenthesis
S o comma space t h e space p e r i o d space o f space f left parenthesis x right parenthesis space i s space straight pi.
    General
    physics-

    In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volt and has no ingternal resistance)

    In the given circuit, resistors 4R and 2R are connected in parallel while resistance R is connected in series to it.
    Hence, equivalent resistance is

    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 R end fraction plus fraction numerator 1 over denominator 2 R end fraction
    equals fraction numerator 6 R over denominator 8 R to the power of 2 end exponent end fraction
    R to the power of ´ end exponent equals fraction numerator 8 over denominator 6 end fraction R
    equals fraction numerator 4 over denominator 3 end fraction R
    ⟹ R to the power of ´ ´ end exponent equals R plus fraction numerator 4 over denominator 3 end fraction R equals fraction numerator 7 R over denominator 3 end fraction
    Given, emf is E volts, therefore
    i equals fraction numerator E over denominator R end fraction equals fraction numerator 3 E over denominator 7 R end fraction

    Potential difference across R is
    V equals i r equals fraction numerator 3 R over denominator 7 R end fraction cross times R equals fraction numerator 3 E over denominator 7 end fraction
    Potential difference across 2R is
    V to the power of ´ end exponent equals E minus fraction numerator 3 E over denominator 7 end fraction equals fraction numerator 4 E over denominator 7 end fraction

    In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volt and has no ingternal resistance)

    physics-General
    In the given circuit, resistors 4R and 2R are connected in parallel while resistance R is connected in series to it.
    Hence, equivalent resistance is

    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 R end fraction plus fraction numerator 1 over denominator 2 R end fraction
    equals fraction numerator 6 R over denominator 8 R to the power of 2 end exponent end fraction
    R to the power of ´ end exponent equals fraction numerator 8 over denominator 6 end fraction R
    equals fraction numerator 4 over denominator 3 end fraction R
    ⟹ R to the power of ´ ´ end exponent equals R plus fraction numerator 4 over denominator 3 end fraction R equals fraction numerator 7 R over denominator 3 end fraction
    Given, emf is E volts, therefore
    i equals fraction numerator E over denominator R end fraction equals fraction numerator 3 E over denominator 7 R end fraction

    Potential difference across R is
    V equals i r equals fraction numerator 3 R over denominator 7 R end fraction cross times R equals fraction numerator 3 E over denominator 7 end fraction
    Potential difference across 2R is
    V to the power of ´ end exponent equals E minus fraction numerator 3 E over denominator 7 end fraction equals fraction numerator 4 E over denominator 7 end fraction
    General
    physics-

    In the adjoining figure the equivalent resistance between A and B is

    Equivalent circuit of the given circuit is

    Between points C and D resistors 2capital omega, 2capital omega and 2capital omega are in series, therefore, their equivalent resistance,
    R to the power of ´ end exponent equals 2 plus 2 plus 2 equals 6 capital omega
    Resistors R’ and 6capital omega are in parallel, therefore their equivalent resistance is given by
    fraction numerator 1 over denominator R to the power of ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction
    R to the power of ´ ´ end exponent equals 3 capital omega
    Now between points A and B 1capital omega, 3blank capital omega and 1capital omega are in series.
    Therefore, resultant resistance is
    R=1+3+1=5capital omega

    In the adjoining figure the equivalent resistance between A and B is

    physics-General
    Equivalent circuit of the given circuit is

    Between points C and D resistors 2capital omega, 2capital omega and 2capital omega are in series, therefore, their equivalent resistance,
    R to the power of ´ end exponent equals 2 plus 2 plus 2 equals 6 capital omega
    Resistors R’ and 6capital omega are in parallel, therefore their equivalent resistance is given by
    fraction numerator 1 over denominator R to the power of ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction
    R to the power of ´ ´ end exponent equals 3 capital omega
    Now between points A and B 1capital omega, 3blank capital omega and 1capital omega are in series.
    Therefore, resultant resistance is
    R=1+3+1=5capital omega
    General
    physics-

    The charge on the capacitor of capacitance C shown in the figure below will be

    The charge on the capacitor of capacitance C shown in the figure below will be

    physics-General
    General
    physics-

    Each resistance shown in figure is 2blank capital omega. The equivalent resistance between A and B is

    Given circuit is a balanced Wheatstone bridge. So, diagonal resistance of 2capital omega will be ineffective.

    Equivalent resistance of upper arms
    =2+2=4capital omega
    Equivalent resistance of lower arms
    =2+2=4capital omega
    R subscript A B end subscript equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction equals 2 capital omega

    Each resistance shown in figure is 2blank capital omega. The equivalent resistance between A and B is

    physics-General
    Given circuit is a balanced Wheatstone bridge. So, diagonal resistance of 2capital omega will be ineffective.

    Equivalent resistance of upper arms
    =2+2=4capital omega
    Equivalent resistance of lower arms
    =2+2=4capital omega
    R subscript A B end subscript equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction equals 2 capital omega
    General
    physics-

    The equivalent resistance across A and B is

    The equivalent circuit can be redrawn as

    we have, fraction numerator P over denominator Q end fraction equals fraction numerator R over denominator S end fraction
    i e comma blank fraction numerator 4 over denominator 4 end fraction equals fraction numerator 4 over denominator 4 end fraction
    So, the given circuit is a balanced Wheatstone’s bridge.
    Hence, the equivalent resistance
    R subscript A B end subscript equals fraction numerator open parentheses 4 plus 4 close parentheses cross times open parentheses 4 plus 4 close parentheses over denominator open parentheses 4 plus 4 close parentheses plus open parentheses 4 plus 4 close parentheses end fraction
    equals fraction numerator 8 cross times 8 over denominator 8 plus 8 end fraction equals fraction numerator 64 over denominator 16 end fraction equals 4 capital omega

    The equivalent resistance across A and B is

    physics-General
    The equivalent circuit can be redrawn as

    we have, fraction numerator P over denominator Q end fraction equals fraction numerator R over denominator S end fraction
    i e comma blank fraction numerator 4 over denominator 4 end fraction equals fraction numerator 4 over denominator 4 end fraction
    So, the given circuit is a balanced Wheatstone’s bridge.
    Hence, the equivalent resistance
    R subscript A B end subscript equals fraction numerator open parentheses 4 plus 4 close parentheses cross times open parentheses 4 plus 4 close parentheses over denominator open parentheses 4 plus 4 close parentheses plus open parentheses 4 plus 4 close parentheses end fraction
    equals fraction numerator 8 cross times 8 over denominator 8 plus 8 end fraction equals fraction numerator 64 over denominator 16 end fraction equals 4 capital omega
    General
    physics-

    Figures i) and ii) below show the displacement-time graphs of two particles moving along the x-axis. We can say that

    Figures i) and ii) below show the displacement-time graphs of two particles moving along the x-axis. We can say that

    physics-General
    General
    physics-

    The graph of displacement v divided by s time is

    Its corresponding velocity-time graph will be

    We know that the velocity of body is given by the slope of displacement – time graph so it is clear that initially slope of the graph is positive and after some time it becomes zero (corresponding to the peak of graph) and it will become negative

    The graph of displacement v divided by s time is

    Its corresponding velocity-time graph will be

    physics-General
    We know that the velocity of body is given by the slope of displacement – time graph so it is clear that initially slope of the graph is positive and after some time it becomes zero (corresponding to the peak of graph) and it will become negative
    General
    Maths-

    Period of fraction numerator 2 sin space 2 x minus 5 cos space 2 x over denominator 7 cos space x minus 8 sin space x end fraction is

    Period of fraction numerator 2 sin space 2 x minus 5 cos space 2 x over denominator 7 cos space x minus 8 sin space x end fraction is

    Maths-General
    General
    physics-

    The current I drawn from the 5V source will be

    The given circuit can be redrawn as

    The current I drawn from the 5V source will be

    physics-General
    The given circuit can be redrawn as
    General
    physics-

    In the circuit given E=0.6V, R subscript 1 end subscript=100capital omega,R subscript 2 end subscript equals R subscript 3 end subscript equals 50 capital omega comma blank R subscript 4 end subscript equals 75 capital omega. The equivalent resistance of the circuit, in ohm is

    R subscript 2 end subscript comma blank R subscript 3 end subscript a n d R subscript 4 end subscript are in parallel order, so their equivalent resistance
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 4 end exponent end fraction
    equals fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 75 end fraction
    equals fraction numerator 30 plus 30 plus 20 over denominator 1500 end fraction
    equals fraction numerator 80 over denominator 1500 end fraction equals fraction numerator 4 over denominator 75 end fraction
    therefore blank R to the power of ´ end exponent equals fraction numerator 75 over denominator 4 end fraction capital omega
    R equals R subscript 1 end subscript plus R to the power of ´ end exponent equals 100 plus fraction numerator 75 over denominator 4 end fraction
    equals fraction numerator 475 over denominator 4 end fraction capital omega equals 118.75 capital omega

    In the circuit given E=0.6V, R subscript 1 end subscript=100capital omega,R subscript 2 end subscript equals R subscript 3 end subscript equals 50 capital omega comma blank R subscript 4 end subscript equals 75 capital omega. The equivalent resistance of the circuit, in ohm is

    physics-General
    R subscript 2 end subscript comma blank R subscript 3 end subscript a n d R subscript 4 end subscript are in parallel order, so their equivalent resistance
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 4 end exponent end fraction
    equals fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 75 end fraction
    equals fraction numerator 30 plus 30 plus 20 over denominator 1500 end fraction
    equals fraction numerator 80 over denominator 1500 end fraction equals fraction numerator 4 over denominator 75 end fraction
    therefore blank R to the power of ´ end exponent equals fraction numerator 75 over denominator 4 end fraction capital omega
    R equals R subscript 1 end subscript plus R to the power of ´ end exponent equals 100 plus fraction numerator 75 over denominator 4 end fraction
    equals fraction numerator 475 over denominator 4 end fraction capital omega equals 118.75 capital omega
    General
    physics-

    Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

    R subscript P Q end subscript equals fraction numerator 5 over denominator 11 end fraction r comma blank R subscript Q R end subscript equals fraction numerator 4 over denominator 11 end fraction r a n d R subscript P R end subscript equals fraction numerator 3 over denominator 11 end fraction r
    therefore R subscript P Q end subscriptis maximum.

    Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

    physics-General
    R subscript P Q end subscript equals fraction numerator 5 over denominator 11 end fraction r comma blank R subscript Q R end subscript equals fraction numerator 4 over denominator 11 end fraction r a n d R subscript P R end subscript equals fraction numerator 3 over denominator 11 end fraction r
    therefore R subscript P Q end subscriptis maximum.
    General
    physics-

    In the circuit shown the equivalent resistance between A and B is

    The three resistances between A and B are parallel,
    fraction numerator 1 over denominator R subscript c o m b end subscript 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 9 end fraction plus fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction
    fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 3 over denominator 9 end fraction
    ⟹ R subscript c o m b end subscript equals 3 capital omega

    In the circuit shown the equivalent resistance between A and B is

    physics-General
    The three resistances between A and B are parallel,
    fraction numerator 1 over denominator R subscript c o m b end subscript 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 9 end fraction plus fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction
    fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 3 over denominator 9 end fraction
    ⟹ R subscript c o m b end subscript equals 3 capital omega
    General
    physics-

    In the circuit shown, the currents i subscript 1 end subscript blank a n d blank i subscript 2 end subscriptare

    R equals fraction numerator 12 cross times 4 over denominator 12 plus 4 end fraction plus 2 equals 5 capital omega
    I equals fraction numerator E over denominator R plus r end fraction equals fraction numerator 12 over denominator 6 end fraction equals 2 A
    I subscript 1 end subscript plus I subscript 1 end subscript equals 2 A
    I proportional to fraction numerator 1 over denominator R end fraction
    therefore I subscript 1 end subscript equals 0.5 A comma blank I subscript 2 end subscript equals 1.5 A

    In the circuit shown, the currents i subscript 1 end subscript blank a n d blank i subscript 2 end subscriptare

    physics-General
    R equals fraction numerator 12 cross times 4 over denominator 12 plus 4 end fraction plus 2 equals 5 capital omega
    I equals fraction numerator E over denominator R plus r end fraction equals fraction numerator 12 over denominator 6 end fraction equals 2 A
    I subscript 1 end subscript plus I subscript 1 end subscript equals 2 A
    I proportional to fraction numerator 1 over denominator R end fraction
    therefore I subscript 1 end subscript equals 0.5 A comma blank I subscript 2 end subscript equals 1.5 A