Starting at t = 0 , the acceleration of a cart varies with time as shown in the figure. Determine the distance travelled in 30 seconds and select the correct description of its position-time graph.

Step-by-step solution

Assuming the cart starts from rest, the initial velocity is u = 0 . For the time interval 0 t 10 s : Acceleration a₁ = 5 ft/s ^2 . Velocity at t = 10 s is v₁ = u + a₁ t = 0 + 5 10 = 50 ft/s . Distance travelled s₁ = 1 2 a₁ t^2 = 1 2 5 (10)^2 = 250 ft . Since acceleration is constant and non-zero, the position-time graph is a parabola. For the time interval 10 Acceleration a₂ = 0 ft/s ^2 . The cart moves with a constant velocity v₂ = 50 ft/s . Distance travelled s₂ = v₂ t = 50 10 = 500 ft . Since velocity is constan