Distance, Velocity, Acceleration, and Rectilinear

Question

A particle moves with velocity function v(t) = 2t² - 3t - 3, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 2 seconds

Options:

1. 3/4 feet per second²
2. -1 feet per second²
3. 32 feet per second²
4. 5 feet per second²

Answer 1

Since acceleration is a rate of change in velocity, then an acceleration function is the derivative of the velocity function. Given that v(t) = 2t² - 3t - 3, then v'(t) = 4t - 3 (by the power rule and constant rule). Then all that remains is to plug in 2 for t.

4(2) - 3 = 5 feet per second²