A car is moving up the plane. Angle of inclination is `theta` and coeffcient of friction is `mu`
(a)What is the condition in which car can be acceleration?
If this condition is satisfied then find (b) maximum acceleration of the car.
(c) minimum retardation of the car.
(d) maximum retardation of the car.

Explanation

(a)`mg sintheta` in all condition is downwards but direction of friction may be upwards or doenwards. We will have to press accelerator for upward friction and brakes for downwards friction.

To accelerated the car friction should be upwards .Therefore car can be accelerated if maximum upwards friction `gt mg sin theta`
or `mumg cos theta gt mg sin theta` or `mugttan theta`
(b) Maximum acceleration `=("maximum upwards force")/("mass")`
`=(mumg cos theta - mg sin theta )/(m) = (mu g cos theta - mg sin theta )`
(c) minimum retardation will be zero , when upward friction `= mg sin theta`
(d)maximum retardation `= ("maximum upwards force")/(m)`
`=(mg sin theta + mu mg cos theta)/(m)`
`=(g sin theta + mu g cos theta)`
This is the case ,when maximum friction force acts in downward direction.