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.

Question

Physics

Reese Stanley

3 February, 09:06

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.

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Philip Arnold · 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