A particle moves in a circle of radius 20 cm. Its linear speed is given by v=2t, where t is in second and v in metre/ second. Find the radial and tangential acceleration at t=3s.

Options

A. `10m/s^2` , `2m/s^2`
B. `100m/s^2` , `12m/s^2`
C. `100m/s^2` , `5m/s^2`
D. `180m/s^2` , `2m/s^2`

Answer

D

Explanation

The linear speed at t=3sis
`v=2t=6m/s`
The radia acceleration at t=3s is
`a_r=v62/r=(36m^2/s^2)/(0.20m)=180m/s^2`
the tangential acceleraton is
` a_t=(dv)/(dt)=(d(2t))/(dt)=2m/s^2`