Question #118075

A body of weight W = 120N is pushed by a horizontal for P = t2 + 6. A frictional force f= t3- 5 resists

its motion. If the body starts from rest, find the velocity of the body after 3 seconds.

its motion. If the body starts from rest, find the velocity of the body after 3 seconds.

Expert's answer

"F=ma=m\\frac{dv}{dt}\\to v=\\frac{1}{m}\\int F(t)dt"

"v=\\frac{1}{m}\\int (t^2+6-t^3+5)dt=\\frac{1}{m}(t^3\/3+6t-t^4\/4+5t)+C="

"=\\frac{1}{m}(t^3\/3+11t-t^4\/4)+C"

if "t=0" "v=0 \\to" "C=0"

We have

"v=\\frac{1}{m}(t^3\/3+11t-t^4\/4)=\\frac{1}{120\/9.81}(3^3\/3+11\\cdot 3-3^4\/4)=1.78 m\/s"

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