Question

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 (a) Find the velocity and acceleration of the particle.

Answer 1

The position of the particle is given by:

x(t) = t³ - 12t² + 21t - 9

Differentiate x(t) with respect to t to find the velocity x'(t):

x'(t) = 3t² - 24t + 21

Differentiate x'(t) with respect to t to find the acceleration x''(t):

x''(t) = 6t - 24