Question

Given the position function s(t), s(t) = t3 + 4t, where s is measured in meters and t is in seconds, find the velocity and acceleration of the particle at t = 2 seconds.

Answer 1

Velocity = 16 m/s

Acceleration = 12 m/s^2

Explanation:

s(t) = t^3 + 4t

To find the velocity, differentiate s(t) with respect to t.

Velocity = s'(t)

Velocity = 3t^2 + 4

When t = 2

Velocity = 3(2)^2 + 4

= 3(4) + 4

= 12 + 4

= 16 m/s

To find the acceleration differentiate v(t) with respect to t.

acceleration = v'(t)

acceleration = 6t

When t = 2

acceleration = 6(2)

= 12 m/s^2