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

The velocity is the first derivative [s'(t)] and the acceleration is the second derivative [s''(t)].

s'(t) = 2t + 3

so s'(4) = 2(4) + 3 = 11

s''(t) = 2

so s''(4) = 2