Derive the position-velocity relation using a speed-time graph.

 What can you say about the motion of a body from the following velocity-time graphs?

The values of displacement of a body at different instances of time are given below:

(a) Draw the displacement-time graph.

(b) What is the slope of the line obtained?

(c) What is the velocity of the body?
(d) Is the velocity uniform?

(e) Draw the v-t graph.

A body starts from rest and moves with a uniform acceleration of $5 \mathrm{m}/{\mathrm{s}}^2$ for $5 \mathrm{s}$ and then it moves with a constant velocity for $4 \mathrm{s}$. Later it slows down and comes to rest in $5 \mathrm{s}$. Draw the velocity-time graph for the motion of the body and answer the following questions:

(a) What is the maximum velocity attained by the body?

(b) What is the distance travelled during this period of acceleration?

(c) What is the distance travelled when the body was moving with a constant velocity?

(d) What is the retardation of the body while slowing down?

(e) What is the distance travelled while retarding?

(f) What is the total distance travelled?

(g) What is the average velocity of the body during the entire journey?
 

Represent the following displacements graphically.

(a) $5 \mathrm{m}$ in the north-east direction

(b) $10 \mathrm{m}$ in north-west direction

(c) $15 \mathrm{m}$ in the south direction

(d) $6 \mathrm{m}$ in the south-west direction