## Fundamentals of Physics Extended (10th Edition)

$v(4.0)=47m/s$
To find velocity from acceleration, note that $$v(t)=\int a(t) dt$$ Substituting the acceleration function and using power rule to integrate yields $$v(t)=\int 5.0t dt=2.5t^2+C$$ At $t=2.0s$, the velocity is +17m/s. Therefore, it can be said that $$v(2.0)=17m/s$$ Substituting $t=2.0s$ allows one to solve for the value of the constant. $$v(2.0)=17m/s=2.5(2.0s)^2+C$$ $$17-2.5(2.0s)^2=C$$ $$C=7.0$$ Therefore, the velocity function is $v(t)=(2.5t^2+7.0)m/s$. Substituting $t=4.0s$ yields a velocity of $$v(4.0)=2.5(4.0)^2+7.0=47m/s$$