e) A body moves in a straight line so that its distance S meters from a fixed point 0 at time t seconds is given by S=(t-2)^2(2t-7) Find the time when the body passes through point 0 and the acceleration each time it passes through 0. (3 Marks)

To find the time when the body passes through point 0, we need to set the distance S equal to 0 and solve for t. This equation is satisfied when either or . gives . gives .So, the body passes through point 0 at seconds and seconds.To find the acceleration each time the body passes through 0, we need to take the second derivative of the position function S(t) with respect to t. Taking the first derivative: Taking the second derivative: Now, we can evaluate the acceleration at the times when the body passes through point 0:At seconds: m/s²At seconds: m/s²Therefore, the acceleration each time the body passes through point 0 is -6 m/s² at seconds and 12 m/s² at seconds.