Question

A particle's position on the x axis is given by x=5t^3+20t^2-t+10

Fine the particle velocity function v(1)and acceleration a (t)

Answer 1

Velocity is the first derivative of the position:

$$v(t) = 15t^2 + 40t + 1\\ v(1) = 15\cdot 1^2 + 40\cdot 1 + 1 = 56$$

Acceleration is the second derivative of the position:

$$a(t) = 30t + 40$$