Question

A 1.2 x 10^3 kg car accelerates uniformly from 5.0 m/s east to 12 m/s east. During this acceleration the car travels 94 m. What is the net force acting on the car during the acceleration?

I know F=mass x acceleartion.

We have the mass so I need to find the acceleration first. I know acceleration is velocity over time. So 12 m/s - 5 m/s = 7 m/s. We need the time, and I know that time is distance over velocity, so 94m / 7m/s = 13s. Now I can try to find the acceleration. 7m/s / 13s = 0.54 m/s^2. So force = 1200 kg x 0.54 m/s^2. I get 648 N, but the answer is 760 N. What am I doing wrong?

Answer 1

Your calculation isn't quite right. It's true that the CHANGE in velocity is 7 m/s. However, the next equation you have uses velocity, not CHANGE in velocity, because this calculation assumes constant velocity (i.e. NO acceleration) - that means you can't perform the calculation you performed.

Instead, look at the variables you're given to start: initial velocity (vi), final velocity (vf), and distance (d). You are correct that you need to find acceleration (a), so we need an equation that incorporates all four of these variables. The equation you want is this one:

\[v_f^2=v_i^2+2a d\]\[12^2=5^2-2a(94)\]\[a=0\]
Solving that equation gives you an acceleration of 0.63 m/s^2. Now you can sub THAT value into F=ma to find the force, which works out to about 756 N, which (with rounding differences) is close enough to the answer you've provided!