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.

Velocity = 16 m/s

Acceleration = 12 m/s^2

Step-by-step 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