Question

A car traveling at 39 m/s runs out of gas while traveling up a 9.0o slope. How far will it coast (m) before starting to roll back down?

Answer 1

Concepts and reason

The concept required to solve the problem is Kinematics equation.

Initially, draw the free body diagram and show the components of force due to gravity along

Horizontal and vertical axis. Find the acceleration, substitute the values in the equation and find the distance travelled.

Fundamentals

The deceleration a of the body travelling up an incline at angle with horizontal is given as follows:

Here, g is the acceleration due to gravity.

Let the velocity of the body changes from u to v after travelling a distance S by the body. The distance travelled by the body is given by following expression:

Use the expression for deceleration, the distance travelled can be given as follows:

The following figure shows the free body diagram of the car.

Here, mg is the force due to gravity, is the angle of inclination, is the force component along vertical axis and is the force component along horizontal axis.

The expression for calculating the acceleration is given as follows:

Here, F is the component of the weight acting down the incline and m is the mass of the body.

The equation of the motion is given as follows:

Re-arrange the above equation for S.

Substitute for a in equation .

Substitute for v, for u , for g and for in the equation .

Ans:

The distance travelled by the object before starting to roll down is .