A basketball player releases a ball without initial speed. The ball rebounds on the ground. Make a visual representation of the situation, showing the velocity and acceleration during the short time when the ball comes into contact with the ground.

Functions are used to represent various changing quantities as functions of position and time. The dependence of the velocity of a rocket on time is given by a function v_x(t) = a + bt². If a = 20 m/s and b = 0.250 m/s³, graph v_x(t) and a_x(t) for the rocket's motion between t = 0 and t = 8 s.

A car which is initially at rest starts moving and attains its top speed in some time. It then continues to move at that constant speed. Model this movement of the car with the help of a motion diagram.

In an experiment to accelerate an object to the maximum speed in the minimum time possible, researchers find that the object's acceleration follows the relation a₀ = a_x + cv_x, c being a constant and a₀ the starting acceleration. Derive an expression for c using a₀ and the maximum speed, V_max.

Two friends Ricky and Jessie decided to go cycling. Jessie starts driving from her house at a constant speed of 10 m/s, she passes Ricky's house when Ricky begins cycling and he increases his speed at a constant acceleration of 0.5 m/s². Draw a pictorial representation along with a motion diagram of this event from Ricky's house till the point he crosses Jessie.

Show the acceleration vectors along with their direction for the motion diagram given below.