Find the velocity at time t.

Question

Suppose that the position of a particle is given by s = f(t) = 2t³+4t+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/s²

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

____ m/s²

Answer 1

Hi Joshua,

(a)Velocity is the derivative of position with respect to time:

Apply the power rule to the position function: v(t)=6t²+4 m/s

(b) Plug in 3 for "t": 6(3)²+4=58 m/s

(c) Acceleration is the rate of change of velocity with respect to time. Apply the power rule to part (a):

12t m/s²

(d)Plug in 3 for "t" 12(3)=36 m/s²

I hope this helps!