I'm working on Physics homework and have run into a problem I can't figure out. Any help would be much appreciated!
Problem:
Allison exerts a steady net force of 50N on a 22-kg shopping cart initially at rest for 1.2s .
A) Find the acceleration of the cart.
I figured this out just fine. The answer is 2.3 m/s^2.
B) Find a distance it moves.
This is what I tried:
acceleration = change in velocity / change in time
2.3 m/s^2 = change in velocity / 1.2 s
change in velocity = 2.76 m/s
distance = [(initial velocity + final velocity) / 2] x time
distance = (2.76 m/s / 2) x 1.2 s
distance = 1.38 m/s x 1.2 s
distance = 1.656 m
Unfortunately, this is not the correct answer. Any thoughts on what I'm doing incorrectly?
Best Answer
force = acceleration * mass, hence acceleration will be $a=50N/22kg \approx 2.27m/s^2$
Distance it moves might be found by integration: $\int_0^{1.2}v(t)dt=\int_0^{1.2}atdt$, since speed $v(t)=at$
Answer to (B) then is 1/2*1.2*(2.27*1.2)=1.63, which seems pretty close to what you have got