A car is moving along a circular path of radius 500 m with a speed of `30ms^(-1)` If at some instant its speed increases at the rate of `2ms^(2)`, then at that instant the magnitude of resultant acceleration will be

Options

A. `4.7ms^(-2)`
B. `9.8ms^(-2)`
C. `3ms^(-2)`
D. `2.7ms^(-2)`

Answer

D

Explanation

Centripetal acceleration
`a_(c)=(v^(2))/r=((30)^(2))/500=1.8m//s^(2)`
Tangential acceleration `a_(t)=2ms^(-2)`
`:.` Resultant acceleration`a=sqrt(a_(t)^(2)=a_(c)^(2))=sqrt((1.8)^(2)+2^(2))=2.7m//s^(2)`