Effect speed and mass has on stopping distance?

Question

Can you please describe how both speed and mass affect stopping distance? (i know the faster you go and heavier the car is the longer the stopping distance but try to be indepth please)

Answer 1

Newtons 2nd law of motion states that ΣF = ma.

ΣF = sum of all forces

m = mass

a = acceleration

the force involved with stopping distance is called inertia.

inertia is a force, so ΣF will represent inertia.

lets say a car weighs 10kg (yes this is a very small car, but its an example!) and is slowing down at a rate of -2 m/s²

F = ma

F = (10)(-2) = -20N

the force of a light-weight car slowing down is 20N.

now, we'll look at a car that weighs 150kg, slowing down at a rate of -20 m/s²

F = ma

F = (150)(-20) = -3000N

**note: N means newtons, which is kg * m/s² **

As you can see, mass and speed have play a large role in stopping distance.

with the small car, it would take 20N of force to stop, but with the heavier car, it takes 3000N to stop.

hope this helped!

Answer 2

INERTIA!!!!!

Answer 3

kinetic energy of a moving body is mass * velocity squared.

So for example twice the mass has twice the energy,

double the speed has four times the energy.

To bring the body to rest this energy has to expended by a stopping force.   eg car brakes get very hot

Answer 4

When a car is moving, it has Kinetic Energy.

Kinetic Energy  =  0.5 * mass * velocity^2

Suppose that the car takes a distance "d" to stop, and that the brakes exert a stopping force "F"

Work done by this force to stop the car  = force * distance

                                                                     =  F * d

The Kinetic Energy is equal to the work done to stop.

So   F * d  =  0.5 * mass * velocity^2

Distance to stop,  d  =   0.5  *  mass  *  velocity^2 / F

We can now see how the distance to stop is affected by the other quantities:-

If you can e.g. double the braking force, the stopping distance halves, if the others do not change.

If you can make the car lighter, e.g. halve its mass, the stopping distance halves, if the others do not change.

However, if you halve your speed, the stopping distance becomes one quarter ( half squared), if others do not chenge.

Speed , or lack of it, is very important.  ( since velocity is squared here.)

If you travel  2 times faster (double the speed), then you take 4  ( 2 squared)  the distance to stop.

3 times faster, and its 9 times further, etc.

The "easiest" way to cut down your stopping distance is to slow down.

Answer 5

In order to stop a car, the kinetic energy of the moving mass of the car must be converted to heat by friction between the brake pads and the brake discs or drums and/or friction between the tires and the road.

The kinetic energy of the moving mass of the car is given by:

Energy = Mass X Velocity Squared / 2

The energy of the opposing frictional force is given by:

Energy (or work) = Stopping Force X Distance

The kinetic energy of the car is equal to the work done to stop it:

Mass X Velocity Squared / 2 = Force X Distance

Solving for stopping distance:

Distance = Mass X Velocity Squared / 2 X Stopping Force

Therefore, stopping distance is directly proportional to mass, directly proportional to the square of velocity and inversely proportional to stopping force.

If the brakes lock and the car skids, all of the stopping energy is converted to heat by the friction between the tires and the road. That frictional force is directly proportional to the force of the weight of the car pressing the tires against the road. In that case, the mass in the denominator cancels the mass in the numerator and the stopping distance is determined by the speed of the car and the coefficient of friction between the tires and the road.