Test 1 -- Motion in a straight line

1. Consider a car that starts at rest, and gradually speeds up with constant acceleration for \(t_1\) seconds. Then the car travels at that final velocity until time \(t_2\) and finally slows down with constant acceleration, stopping at time \(t_3\). Draw the position-time, velocity-time and acceleration-time graphs describing this.

2. A truck initially at rest travels \(100m\) in \(5 s\). Assuming it's in uniform motion, find the acceleration of the truck. Also find the final velocity of the truck at \(t=5 s\).

3. A ball is dropped from a building, and the velocity of the ball when it hits the ground is \(10\,m/s\). Find the time taken for the ball to reach the ground and also the height of the building. Assume \(g=\,10m/s^2\). [Hint: Initial velocity is 0]