The equation of motion of a particle is s = 2t3 − 6t2 + 3t + 2, where s is in meters and t is in seconds.

Question

The equation of motion of a particle is s = 2t³ − 6t² + 3t + 2, where s is in meters and t is in seconds.

(a) Find the velocity and acceleration as functions of t.

(b) Find the acceleration after 2 s.

Answer 1

The velocity is ds/dt or the derivative of s(t). To find the derivative, use the power rule:

s(t) = 2t³ − 6t² + 3t + 2

s'(t) = 6t² - 12t + 3

so v(t) = 6t² - 12t + 3

The acceleration is dv/dt or the derivative of v(t). To find the derivative, use the power rule:

v(t) = 6t² - 12t + 3

v'(t) = 12t - 12

so a(t) = 12t - 12

a(2) = 12(2) - 12 = 24 - 12 = 12 m/s²