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

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