A jeep turns around a curve of radius 0.3 km at a constant speed of 60 m/s. The resultant change in velocity, instantaneous acceleration and average acceleration over `60^(@)` arc are

Options

A. `30ms^(-1),11.5ms^(-2),12ms^(-2)`
B. `60ms^(-1),12ms^(-2),11.5ms^(-2)`
C. `60ms^(-1),11.5ms^(-2),12ms^(-2)`
D. `40ms^(-1),10ms^(-2),8ms^(-2)`

Answer

B

Explanation

`Deltavecv=vecv_(1)-vecv_(2)," "Deltav=(v_(1)^(2)+v_(2)^(2)-2v_(1)v_(2)cos 120)^(1//2)`
`=[60^(@)+60^(2)-2xx60xx60xx1/2]^(1//2)=60m//s`
Instantaneous acceleration `=(v^(2))/r=(60^(@))/(0.3xx1000)=12m//s^(2)`
Time taken to cover the arc `t=(pi)/3xx300/60:.(t=s/v=(r d theta)/v)`
`:.` average acceleration `a=(Deltav)/t=60/((pi)/3xx300/60)=11.5m//s^(2)`