A motor car travelling at `30 m//s` on a circular road of radius `500m`. It is increasing its speed at the rate of `2 ms^(-2)`. What its accleration at that instant ?

Options

A. `1.8ms^(-2)`
B. `2ms^(-2)`
C. `3.8ms^(-2)`
D. `2.7ms^(-2)`

Answer

d

Explanation

Radial acceleration `a_(r)=(v^(2))/r=((30)^(2))/500=1.8ms^(-2)`
Tangential acceleration at `=2m//sec^(2)`
Resultant acceleration
`a^(2)=a_(r)^(2)+a_(t)^(2)+2a_(r)a_(t)cos theta`
Here, `theta=90^(@)`
`a^(2)=(1.8)^(2)+(2)^(2)+0=3.24+4=7.24`
`a=sqrt(7.24)=2.7 ms^(-2)`