A car accelerates from rest at a constant rate `alpha` for some time afrer which it dccelerates at a constant rate of `beta` to come to rest , If the total time elapsed is `t` second, then calculat
a. the maximum velocity attained by the car, and
b. the total displacement travelled by the car in terms of `alpha , beta` and `t`.

Options

A. v
B. `(pi//4)v`
C. `(4//pi)v`
D. Zero

Answer

C

Explanation

Relative velocityt, `v_(r)=|vec(v)_(1)-vec(v)_(2)|` where `v_(1)=v_(2)=v`
If angle between them be `theta`, then `v_(r)=sqrt(v^(2)+v^(2)-2v^(2) cos theta)=sqrt(2v^(2)(1-cos theta))=2v sin (theta/2)`
Hence, average relative velocity `vec(v)_(r)=(underset(0)overset(2pi)(int)2v" sin"theta/2d theta)/(underset(0)overset(2pi)(int)d theta)=(4v)/pi`