A car starts moving rectilinearly, first with acceleration $\alpha =$ $5 \mathrm{m}{ \mathrm{s}}^{-2}$ (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate $\alpha$ comes to a stop. The total time of motion equals $t=25 \mathrm{s}$. The average velocity during this time is equal to $<v>=72 \mathrm{km}{ \mathrm{h}}^{-1}.$ How long does the car move uniformly?

A hot-air balloonist rising vertically with a constant velocity of magnitude $20{ \mathrm{m} \mathrm{s}}^{-1}$, releases a sandbag at an instant when the balloon is $25 \mathrm{m}$ above the ground (figure). After it is released, the sandbag is in free fall. Sketch $a_{\mathrm{y}}-t, v_{\mathrm{y}}-t$ and $\left|v_{\mathrm{y}}\right|-t$ graphs for the motion, taking origin at ground.

At the height of $75 \mathrm{m}$, a particle $A$ is thrown up with $u_{\mathrm{A}}=10{ \mathrm{m} \mathrm{s}}^{-1}$ and $B$ particle is thrown down with $u_{\mathrm{B}}=10{ \mathrm{m} \mathrm{s}}^{-1}$ and $C$ particle released with $u_{\mathrm{C}}=0{ \mathrm{m} \mathrm{s}}^{-1}$. Draw graphs of each particle.

(a) Displacement-time
(b) Speed-time
(c) Velocity-time
(d) Acceleration-time

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.