Question

The acceleration of a point is a= 20t m/s2. When t= 0, x= 40 m and v= - 10 m/s. What are the position and velocity at t= 3 s?

Answer 1

$v(t)=\int adt=10t^2+c_1,$

$c_1=-10~\frac ms,$

$v(t)=10t^2-10,$

$x(t)=\int vdt=\frac{10}3 t^3-10t+c_2,$

$c_2=40~m,$

$x(t)=\frac{10}3t^3-10t+40,$

$x(3)=100~m,~v(3)=80~\frac ms.$