Physics-
General
Easy
Question
The graph of displacement-time for a body travelling in a straight line is given. We can conclude that
![](data:image/png;base64,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)
- The velocity is constant
- The velocity increases uniformly.
- The body is subjected to acceleration from
to
.
- The velocity of the body at
is zero.
The correct answer is: The velocity of the body at
is zero.
At the point
, the tangent to the curve is parallel to time axis. So, velocity at
is zero. But acceleration is not zero. Note that the displacement corresponding to the point
is not zero.
Related Questions to study
physics-
A particle moves along
-axis as
Which of the following is true
A particle moves along
-axis as
Which of the following is true
physics-General
physics-
Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is
![](data:image/png;base64,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)
Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is
![](data:image/png;base64,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)
physics-General
maths-
The equation
where χ is a variable with real roots, then the interval of p may be any one of the following
The equation
where χ is a variable with real roots, then the interval of p may be any one of the following
maths-General
physics-
An engine is moving on a circular track with a constant speed. It is blowing a whistle of frequency
The frequency received by an observer standing stationary at the centre of the track is
![](data:image/png;base64,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)
An engine is moving on a circular track with a constant speed. It is blowing a whistle of frequency
The frequency received by an observer standing stationary at the centre of the track is
![](data:image/png;base64,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)
physics-General
physics-
In Young’s experiment, monochromatic light is used to illuminate the two slits A and B. Interference fringes are observed on a screen placed in front of the slits. Now if a thin glass plate is placed normally in the path of the beam coming from the slit
![](data:image/png;base64,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)
In Young’s experiment, monochromatic light is used to illuminate the two slits A and B. Interference fringes are observed on a screen placed in front of the slits. Now if a thin glass plate is placed normally in the path of the beam coming from the slit
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the acceleration-time graphs of a particle. Which of the following represents the corresponding velocity-time graphs?
![](data:image/png;base64,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)
Figure shows the acceleration-time graphs of a particle. Which of the following represents the corresponding velocity-time graphs?
![](data:image/png;base64,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)
physics-General
maths-
If
and
, then the possible values of χ between
and
are
If
and
, then the possible values of χ between
and
are
maths-General
maths-
A) Area bounded by = 2 and coordinate axes
B) Area bounded by
and ![x to the power of 2 end exponent equals 4 y](data:image/png;base64,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)
C) Area bounded by
between x=0,x=1,x- axis
D) Area bounded by
and y=2x Arrange the above statements in the ascending order of areas.
A) Area bounded by = 2 and coordinate axes
B) Area bounded by
and ![x to the power of 2 end exponent equals 4 y](data:image/png;base64,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)
C) Area bounded by
between x=0,x=1,x- axis
D) Area bounded by
and y=2x Arrange the above statements in the ascending order of areas.
maths-General
Physics-
Velocity-time
-
graph for a moving object is shown in the figure. Total displacement of the object during the same interval when there is non-zero acceleration and retardation is
![](data:image/png;base64,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)
Velocity-time
-
graph for a moving object is shown in the figure. Total displacement of the object during the same interval when there is non-zero acceleration and retardation is
![](data:image/png;base64,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)
Physics-General
physics-
A particle moves along the sides
of a square of side
wuth a velocity of
. Its average velocity is
![](data:image/png;base64,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)
A particle moves along the sides
of a square of side
wuth a velocity of
. Its average velocity is
![](data:image/png;base64,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)
physics-General
physics-
The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in
are respectively
![](data:image/png;base64,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)
The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in
are respectively
![](data:image/png;base64,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)
physics-General
maths-
The area bounded by
, Y-axis and the line y=e is
The area bounded by
, Y-axis and the line y=e is
maths-General
maths-
If
then the general value of 'α ' is
If
then the general value of 'α ' is
maths-General
maths-
The parabolas
divide the square region bounded by the lines x=4, y=4 and the co-ordinate axes. If
are respectively the areas of these parts numbered from top to bottom then
is
The parabolas
divide the square region bounded by the lines x=4, y=4 and the co-ordinate axes. If
are respectively the areas of these parts numbered from top to bottom then
is
maths-General
physics-
The figure shows a double slit experiment P and Q are the slits. The path lengths PX and QX are
and
respectively, where n is a whole number and
is the wavelength. Taking the central fringe as zero, what is formed at X
![](data:image/png;base64,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)
The figure shows a double slit experiment P and Q are the slits. The path lengths PX and QX are
and
respectively, where n is a whole number and
is the wavelength. Taking the central fringe as zero, what is formed at X
![](data:image/png;base64,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)
physics-General