A car is travelling at a speed of 21.6 km/hr when it reaches a 12.8 m long slope with an inclination of 30^ , as shown in the figure. The coefficient of friction between the tyre and the road is 1 2 3 . Determine the minimum possible speed with which the car can reach the bottom, regardless of how hard the driver applies the brakes. Take g = 10 m/s ^2 .

Step-by-step solution

Initial speed of the car, u = 21.6 km/hr = 21.6 5 18 m/s = 6 m/s . To reach the bottom with the minimum possible speed, the driver must apply the brakes as hard as possible, which means the maximum frictional force will act opposite to the direction of motion (up the slope). The forces acting on the car along the slope are the component of gravity downwards and the frictional force upwards. The net acceleration a down the slope is given by: a = g - g Given = 30^ , = 1 2 3 , and g = 10 m/s ^2 : a = 10 ( 30^ - 1 2 3