Constant Acceleration?

Question

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 meters, with an initial velocity of +5.0m/s and a constant acceleration due to the fan. The direction to the right is positive. The cart reaches a maxmum position of x=+12.5 meters, where it begins to travel in the negative direction. Find the acceleration of that cart.

Im really confused by these problems so if someone could help me out with detailed steps, that would be great!

Answer 1

S=V(0)t - 0.5 at^2

We know that acceleration
a= [V(0) – V(t) ]/t since it reverces direction it must stop at time t then V(t)=0
we have
a= V(0)/t does not help since we do not know t
so t = V(0)/a

now we know that
S=[V(average) ] t that is S (the 12.5 m)
V(average)= [V1+V2]/2 or
V(average)= [V(0) + V(t) ]/2 since V(t)=0
V(average)= 0.5 V(0) or
S=V(0) t or t=S/V(0)

Earlier t = V(0)/a and now t=S/V(0)
V(0)/a=S/V(0)
a=V(0)^2 / S= 25/12.5= 2 m/s

Answer 2

The previous answerer is wrong because this question mentions nothing of time. Use the other kinematic equation:

v_f ^2 = v_i ^2 + 2ad

where vf is final velocity ( zero in your case) vi is the inital velocity, d is the distance you've travelled (12.5m) and a is the acceleration. The only unknown here for you is 'a'. Simply solve for a and you're done.


You should get a negative value for a. This is because the cart is slowing down as it starts at 5 m/s and slows to 0 m/s at a distance of 12.5m

Edit: The answerer below me is also correct. Doing it my way or his/hers will give you the same (correct) answer.

Answer 3

Constant acceleration means a linear velocity.
First we determine the time to get to x=12.5m and v=0m/s
The area under the velocity curve is equal to the distance traveled. This area with be a triangle with height 5m/s and length T.
12.5m = 1/2 5 m/s * T s (equation of a triangle)
T = 5s
The acceleration is the change in velocity / time
=(0-5)/5s = - 1m/s^2