Linear motion with variable forces

jiayingsim123

1. The problem statement, all variables and given/known data
A car of mass 1200kg is at rest on a level road. Two people push it, producing a total force given by (240-12t) newtons, where t is the time in seconds, until this becomes zero after 20 seconds. How fast is the car then moving, and how far does it move while it is being pushed.


3. The attempt at a solution
I got the answer for the first part of the question, which asks how fast the car is then moving, but I can't get the answer for the second part of the question. I got 80/3m instead of 8/3m as stated in the book. Here is my attempt at the question.
m=1200kg
F=(240-12t)N
F=ma
a=F/m=0.2-0.01t

v=∫0.2-0.01tdt (with upper limit=20 and lower limit 0)
= [0.2t-(0.01t^2)/2] (with upper limit=20 and lower limit=0)
= 4-2
= 2 (this is the correct answer)

s = ∫0.2t-(0.01t^2)/2dt (with upper limit=20 and lower limit=0)
= 80/3m

Please include detailed explanations along with your solution, thanks! :D

LawrenceC

I get 26.67 m for the answer, same as you. Look at the result from a kinetic energy standpoint to see who is right or wrong. You have the velocity so you can easily determine the kinetic energy. Take your two possible answers in meters and divide each into the kinetic energy. Which falls in the force bracket when you evaluate the force function?

Infinitum

Hi jiayingsim123. Welcome to PF

I think your answer is correct, and probably just is a small typo in the book.