Graphical Representation of Linear Motion

A ball moves on a smooth floor in a straight line with a uniform velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$ for $6 \mathrm{s}$. At $t\mathit{=}6 \mathrm{s}$, the ball hits a ball and come back along the same line to the starting point with same speed. Draw the velocity-time graph and use it to find the total distance travelled by the ball and its displacement.

The figure shows velocity-time graph for the motion of a body. Use it to find the displacement of the body at $t= 1 \mathrm{s}, 2 \mathrm{s},3 \mathrm{s}$ and $4 \mathrm{s}$, then draw displacement-time graph for it on figure (b).

A body is at rest is made to fall from the top of a tower. Its displacement at different instants is given in the following table

Draw a displacement-time graph and state whether the motion is uniform or non-uniform?

Figure shows the displacement of a body at different times

Calculate the average velocity during the time interval $5 \mathrm{s}$ to $9 \mathrm{s}$.

For the uniform motion :
 

For a uniformly retarded motion, the velocity-time graph is :

The velocity-time graph of a body in motion is a straight line inclined to the time axis. The correct statement is :
 

A body falls freely from a certain height. Show graphically the relation between the distance fallen and the square of time. How will you determine $g$ from this graph?

Figure (a) shows the displacement-time graph for the motion of a body. Use it to calculate the velocity of a body $t=1 \mathrm{s}, 2 \mathrm{s}$ and $3 \mathrm{s}$, then draw the velocity-time graph for it in figure (b).

How is the distance related to time for the motion under uniform acceleration such as the motion of a freely falling body?

Draw a velocity-time graph for the free fall of a body under gravity, starting from rest $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

Draw a graph for acceleration against time for a uniformly accelerated motion. How can it be used to find the change in speed in a certain interval of time?

The figure shows the displacement-time graph for four bodies A, B, C, and D. In each case state what information you get about the acceleration (zero, positive or negative).

The velocity-time graph for a uniformly retarded body is a straight line inclined to the time axis with an obtuse angle. How is retardation calculated from the velocity-time graph?

The figure shows the velocity-time graph for two cars A and B moving in the same direction. Which car has the greater acceleration? Give reason to your answer.

Draw a velocity-time graph for a body moving with an initial velocity $u$ and uniform acceleration $a$. Use this graph to find the distance travelled by the body in time $t$.

The figure shows a displacement-time graph of two vehicles A and B moving along a straight road. Which vehicle is moving faster? Give reason.

What does the slope of the velocity-time graph represent?

Draw a displacement-time graph for a boy going to school with a uniform velocity.

Can the displacement-time sketch be parallel to the displacement axis? Give a reason for your answer.