A car is moving with speed `30m//sec` on a circular path of radius 500 m . Its speed is increasing at the rate of , `2m//sec^(2)`, What is the acceleration of the car

Options

A. `2m//s^(2)`
B. `9.8m//s^(2)`
C. `2.7m//s^(2)`
D. `1.8 m//s^(2)`

Answer

C

Explanation

The car Is moving with an increasing speed and it has tangential accleration `a _(T ) = 2m//s^2`
Similarly it has the centripetal ( radial ) accleration ,
`a_(R ) =(v^(2) )/(r ) =(30xx30)/(500) -(9)/(5)`
As `a_(R ) and a_(T )` are perpendicular to each other
Resultant acceleration `= sqrt(a_(T)^(2) +a_(R )^(2))`
`=sqrt(4+(81)/(25))=sqrt((181)/(25))`
`underset(*) overset(*)=2.7m//s^(2)`