A Car Coasts Engine Off Up a 30 Degree Grade

Introduction

When a car coasts engine off up a hill, it is using its own momentum to carry it forward. The car’s speed will decrease as it climbs the hill, and it will eventually come to a stop if the hill is steep enough.

The rate at which the car’s speed decreases depends on several factors, including the car’s weight, the hill’s grade, and the coefficient of friction between the car’s tires and the road.

Calculating the Car’s Speed

The following equation can be used to calculate the car’s speed as it coasts up a hill:

v^2 = u^2 + 2as

where:

* v is the car’s speed at the top of the hill
* u is the car’s speed at the bottom of the hill
* a is the acceleration due to gravity (9.8 m/s^2)
* s is the distance traveled up the hill

If the car starts from rest at the bottom of the hill, then u = 0 and the equation can be simplified to:

v = sqrt(2as)

Example

Let’s say that a car is coasting up a 30 degree grade. The car weighs 1000 kg and the coefficient of friction between the car’s tires and the road is 0.1.

The distance traveled up the hill is:

s = h / sin(theta)

where:

* h is the height of the hill
* theta is the angle of the hill

In this case, h = 100 m and theta = 30 degrees, so:

s = 100 m / sin(30 degrees) = 200 m

The acceleration due to gravity is:

a = g * sin(theta)

where:

* g is the acceleration due to gravity (9.8 m/s^2)

In this case, theta = 30 degrees, so:

a = 9.8 m/s^2 * sin(30 degrees) = 4.9 m/s^2

The car’s speed at the top of the hill is:

v = sqrt(2as)

where:

* a = 4.9 m/s^2
* s = 200 m

Plugging these values into the equation, we get:

v = sqrt(2 * 4.9 m/s^2 * 200 m) = 22.1 m/s

Therefore, the car’s speed at the top of the hill is 22.1 m/s, or approximately 50 mph.

Conclusion

The rate at which a car’s speed decreases as it coasts up a hill depends on several factors, including the car’s weight, the hill’s grade, and the coefficient of friction between the car’s tires and the road.

By understanding these factors, you can better predict how your car will perform when coasting up a hill.