A particle moves in a straight line for 20 seconds with velocity 3 m/s and then moves with velocity 4 m/s for another 20 seconds and finally moves with velocity 5 m/s for next 20 seconds. What is the average velocity of the particle ?

Options

A. `6 hat(i)`
B. `-15 hat(i)`
C. `10 hat(i)`
D. `-5 hat(i)`

Answer

D

Explanation

Let acceleration of B `vec(a)_(B)=a_(B) hat(i)`
Then acceleration of A w.r.t.
`B=vec(a)_(A)-vec(a)_(R)=(15-a_(B))hat(i)+15 hat(j)`
This acceleration must be along the inclined pplane
so `tan 37^(@)=15/(15-a_(B))rArr 3/4=15/(15-a_(B)) a_(B)=-5`
`rArr vec(a)_(R)=-5hat(i)`