The brakes applied to a car produce an acceleration of $6 \, m s^{-2}$ in the opposite direction of motion. If the car takes $2 \, s$ to stop after the application of the brakes,calculate the distance it travels during this time. (in $, m$)

$A$ person is running along a circular path in a park.
$(a)$ At what point does he change his direction while running?
$(b)$ If he covers half of the circular path,what will be his displacement? Draw a diagram showing it.

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.

What is a velocity-time graph? State how it can be used to find:
$(i)$ The acceleration of a body.
$(ii)$ The displacement of the body.
$(iii)$ The distance travelled in a given time.

Study the speed-time graph of a body given below and answer the following questions:
$(i)$ What type of motion is represented by $OA$,$AB$ and $BC$?
(ii) Find positive and negative accelerations of the body.
(iii) Find the distance travelled by the body from $A$ to $B$.

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.