The $v-s$ and $v^2-s$ graph are given for two particles. Find the accelerations of the particles at $s=0$.

The velocity-displacement for a jet plane on a straight runway is shown in the figure. Determine the speed and acceleration of the jet plane at $s=150 \mathrm{m}$.

Referring to $a-x$ graph, find the velocity when the displacement of the particle is $100 \mathrm{m}$. Assume initial velocity as zero.

Referring to the $v^2-s$ diagram of a particle, find the displacement of the particle during the last $2 \mathrm{s}$.

(a) What can you say about velocity in each of the following position-time graphs?

(i)           (ii)  

(iii)             (iv)   

(v)             (vi)    

(vii)             (viii)  

(b) The slope of the velocity-time graph is equal to acceleration. (True/False)
(c) What does the area under the acceleration-time graph represent?
(d) Can the velocity-time graph be parallel to the velocity axis? (Yes/No). Why?
(e) What is the slope of the $v-t$ graph in uniform motion?

(a)  A ball is thrown vertically upwards. After some time, it returns to the thrower. Draw the velocity-time graph and speed-time graph.

(b) A ball is dropped from some height. After rebounding from the floor, it ascends to the same height. Draw the velocity-time graph and speed-time graph.

A body starts at $t =0$ with velocity $u$ and travels along a straight line. The body has a constant acceleration $a$. Draw the acceleration-time graph, velocity-time graph, and displacement-time graph from $t =0$ to $t=10 \mathrm{s}$ for the following cases: 

(a) $u=8 \mathrm{m} {\mathrm{s}}^{-1}, a=2 \mathrm{m} {\mathrm{s}}^{-2}$

(b) $\mathrm{u}=8 \mathrm{m} {\mathrm{s}}^{-1}, \mathrm{a}=-2 \mathrm{m} {\mathrm{s}}^{-2}$

(c) $u=-8 \mathrm{m} {\mathrm{s}}^{-1}, a=2 \mathrm{m} {\mathrm{s}}^{-2}$

(d) $u=-8 \mathrm{m} {\mathrm{s}}^{-1}, a=-2 \mathrm{m} {\mathrm{s}}^{-2}$

In the given figure, find the average acceleration in first $20 \mathrm{s}$. (Hint: Area under $a-t$ graph is equal to the change in velocity)

At $t = 0$, a particle starts from rest and moves along a straight line, whose acceleration-time graph is shown in the figure.

Convert this graph into a velocity-time graph. From the velocity-time graph, find the maximum velocity attained by the particle. Also, find from, $v-t$ graph, the displacement and distance travelled by the particle from $2$ to $6 \mathrm{s}$.