Answer to Question #79059 in Physics for Vidhi Dixit

Question

At the moment t=0 a stationary particle of mass m experience a time-dependent force F=at(c-t),where a is a constant vector,c is the time during which the given force acts.The distance covered while the force acted is S=(at^N)/P.Find the value of P/N

Answer 1

According to the Newton’s second law we obtain:
m (d^2 x)/(dx^2 )=F=at(c-t)
Integrating this equation two times gives us the following
mx=(act^3)/6-(at^4)/12
x=(act^3)/6m-(at^4)/12m
Since x(t=c)=S, we have
(ac^4)/6m-(ac^4)/12m=(ac^4)/12m=(ac^N)/P
Thus N=4 and P=12m, and we obtain P/N=12m/3=3m.