Calculus Velocity Question

Question

Suppose that the position of a particle is given by s=f(t)=3t^3+7t+9.

(a) Find the velocity at time t.

v(t)=  ___ m/s

(b) Find the velocity at time t=3 seconds.

___ m/s

(c) Find the acceleration at time t.

a(t) =  ____ m/s^2 

(d) Find the acceleration at time t=3 seconds.

 ___ m/s^2

Answer 1

velocity v(t)=s'(t), i.e. the derivative of s.

acceleration a(t) is the derivative of velocity which equals s"(t), the second derivative of s.