Out of the three speed$-$time graphs shown below
Identify the graph for the following cases.
$(i)$ A ball thrown vertically upwards and returning to the hand of the thrower ?
$(ii)$ A body decelerating to a constant speed and accelerating.
$(i)$ Graph $(a)$ shows that the speed of a body decreases with time becomes zero and then again starts increasing. This graph, therefore, represents the case of a ball thrown vertically upwards and then caught by the thrower. Initially, the ball is thrown with some speed. As the ball rises up its speed decreases at a constant rate, becomes and zero at maximum height. The ball then falls with a uniform acceleration till its speed becomes equal to speed of projection.
$(ii)$ Graph $(c)$ represents deceleration of the body to some constant speed, and then accelerating after sometime.
Can you suggest about the kind of motion of a body from following distance$-$time graphs ?
Two stones are thrown vertically upwards simultaneously with their initial velocities $u _{1}$ and $u _{2}$ respectively. Prove that the heights reached by them would be in the ratio of $u_{1}^{2}: u_{2}^{2}$ (Assume upward acceleration is $-\,g$ and downward acceleration to be $+g$.
How can you find the distance travelled by body in uniform motion from the velocity$-$time graph ?
Write true or false for the following statements
Velocity and speed are measured in different units.
What conclusion can you draw from the displacement$-$time graph of a body as shown below ?