A car acceleration form rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta`, to come to rest. If the total time elapsed is t evaluate (a) the maximum velocity attained and (b) the total distance travelled.

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`