A cart is driven by a large propeller or fan, which can accelerate or decelerate the cart. The cart starts out at the position x = 0 m, with an initial velocity of + 5.0 m/s and a constant acceleration due to the fan, The direction to the right is positive. The cart reaches a maximum position of x = + 12.5 m, where it begins to travel in the negative direction. Find the acceleration of the cart.

The acceleration of the cart is 1.0 m/s^2 in the negative direction.

Explanation:

Using the equation of motion:

Vf^2 = Vi^2 + 2*a*x

2*a*x = Vf^2 - Vi^2

a = (Vf^2 - Vi^2) / 2*x

Where Vf is the final velocity of the cart, Vi is the initial velocity of the cart, a the acceleration of the cart and x the displacement of the cart.

Let x = Xf - Xi

Where Xf is the final position of the cart and Xi the initial position of the cart.

x = 12.5 - 0

x = 12.5

The cart comes to a stop before changing direction

Vf = 0 m/s

a = (0^2 - 5^2) / 2*12.5

a = - 1 m/s^2

The cart is decelerating

Therefore the acceleration of the cart is 1.0 m/s^2 in the negative direction.