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

$a (t)= 20t$

$v(t) = \int a(t)dt= 10t^2 +C_1$

$v(0) = -10$

$C_1 = -10$

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

$v(3) = 80\frac{m}{c}$

$x(t) = \int v(t)dt=\frac{10}{3}t^3-10t+C_2$

$x(0) =40$

$C_2 = 40$

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

$x(3) = 120m$

$\text{Answer: }v(3) = 80\frac{m}{s};x(3) = 120m$