Calculus and Acceleration

Question

Let s(t) be an object’s position (in meters) at time t (in seconds), given by

s(t) = 2t^4 + 0.5t^3 − 5t + 7. Determine the object’s acceleration at time t = 1. Be sure

to include appropriate units in your answer.

Answer 1

s(t) = 2t⁴+t³/2-5t+7

v(t) = s'(t) = 8t³+ 3t²/2 - 5

a(t) = v'(t) = 24t² + 3t

a(1) = 24 + 3 = 27 m/s²