Question

At time, t greater than or equal to 0, a particle moving in the xy plane has velocity vector given by v(t)=(t^2, 5t) What is the acceleration vector of the particle at time t=3?"

Answer 1

The acceleration vector of the particle at time t=3 is (6,5).

Explanation:

Acceleration:

The acceleration is the derivative of the velocity.

Derivative of a vector:

To derivate a vector, we derive each component.

v(t)=(t^2, 5t)

So

a(t) = v'(t) = (2t, 5).

What is the acceleration vector of the particle at time t=3?

a(3) = (2*3, 5) = (6,5)

The acceleration vector of the particle at time t=3 is (6,5).