Question

Suppose that the position of a particle is given by s=f(t)=4t^3+3t+9. (a) Find the velocity at time t.(b) Find the velocity at time t=3 seconds.(c) Find the acceleration at time t. (d) Find the acceleration at time t=3 seconds.

Answer 1

s = 4 t^3 + 3 t + 9 position at time t

a) v = ds/dt = 12 t^2 + 3 velocity at time t

b) v = 12 * 3^2 + 3 = 111 velocity at 3 sec

c) a = dv/dt = 24 t

d) a = 72 at 3 sec