Question

A particle moves along the x-axis according to the equation x(t) = 2.0 − 4.0t2 m. What are the velocity and acceleration at t = 2.0 s and t = 5.0 s?

Answer 1

Determine the equations for velocity and acceleration:

$$v(t)=x'(t)=-8t,\\ v(2)=-16\text{ m/s},\\ v(5)=-40\text{ m/s}.\\\space\\ a(t)=v'(t)=-8,\\ a(2)=a(5)=-8\text{ m/s}^2.$$