Find the velocity, acceleration, and speed of a particle with the given position function. r (t) = t i + t2 j + 3 k v (t) = a (t) = Sketch the path of the particle and draw the velocity and acceleration vectors for t = 1.

Velocity

v = i + 2 j

Acceleration

a = 2 j

Explanation:

Given that

r (t) = t i + t² j + 3 k

We know that

Velocity v given as

v = dr/dt

dr/dt = i + 2 t j + 0

v = i + 2 t j

At t = 1

v = i + 2 x 1 j

v = i + 2 j

Acceleration, a

a = dv/dt

v = i + 2 t j

dv/dt = 2 j

a = 2 j