The ball rolling down a hill is accelerated at 3.6 m/s^2. The time required by the ball to travel 400 m has to be determined. It is assumed that the ball starts from rest.
For an object starting with an initial velocity u and traveling for a duration of time t while it is being accelerated at a rate of acceleration equal to a, the distance covered is equal to d = u*t + (1/2)*a*t^2.
Here, the initial velocity is 0. The acceleration is a constant value of 3.6 m/s^2 and the distance covered is 400 m. The time take by the ball to cover the distance is t such that 400 = 0*t + (1/2)*3.6*t^2
=> t^2 = 400*2/3.6
=> t^2 = 2000/9
=> t = 14.90 s
The ball covers the 400 m in a duration of time equal to 14.0 s.