Question

velocity and acceleration of a particle at some instant of time are v=2i-j+2k and ā=î+6j-k. then the speed of the particle is ____at a rate of _____m/s².

Answer 1

Given:

The velocity of the particle v= 2i-j+2k

The acceleration of the particle a= i+6j-k

To find :

The speed of particle at what rate.

Solution:

Calculate the dot product of the v and a

v.a=(2i-j+2k).(i+6j-k)

v.a=2-6-2

v.a=-6 m²/sec³

So the speed is decreasing at the rate of -6m²/sec³