Question

The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time. (b) What are its velocity and acceleration at time t = 0?

Answer 1

Step-by-step explanation:

It is given that,

The position of a particle is given by :

`r(t)=(3t^2i+5j-6tk)\ m`

(a) Velocity of a particle is given by :

`v=(dr(t))/(dt)`

Putting values,

`v=(d)/(dt)(3t^2+5-6t)\\\\v=(6ti-6k)\ m/s`

The acceleration of the particle is given by :

`a=(dv)/(dt)\\\\a=(d)/(dt)(6t-6)\\\\a=6i\ m/s^2`

(b) At t = 0,

Velocity, v = 6k m/s

Acceleration, a = 6i m/s²