Module calculus problem

Question

Given the position function s(t), s(t) = t² + 3t + 1, where s is measured in meters and t is in seconds, find the velocity and acceleration of the particle at t = 4 seconds

Options:

1. 11 m/sec; 2 m/sec²
2. 2 m/sec; 0 m/sec²
3. 11 m/sec; 0 m/sec²
4. 12 m/sec; 2 m/sec²

Answer 1

s(t) = t² + 3t + 1

velocity is the 1st derivative of position, and acceleration is the 2nd derivative.

velocity: v = s' = 2t + 3. At t = 4, v = 11

acceleration: a = 2