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Forces and Motion

The Braking Distance of a Car - Mass.

The total stopping distance = thinking distance + braking distance.

Changing the mass of a car does not change the thinking distance
the braking distance is changed as the mass of a car changes.

See also the calculation of the force need to stop a moving car
using kinetic energy or momentum.

How does Mass affect the Braking Distance of a Car?

The braking distance of a car increases as the mass increases.
The two calculations below show how
doubling the mass changes the braking distance of a car.

.  The brakes of a car apply a force of 1500N.
If the car has a mass of 750 kg, what is its acceleration?
(How quickly does it slow down?)

A1.  Use  F = m x a
or  a = F ÷ m

   a = 1500 ÷ 750
= 2 m/s2.

Strictly speaking we would call the acceleration -2 m/s2
because the car is slowing down.

Q2.  The brakes of the car apply the same force of 1500N.
If the car has double the mass at 1500 kg, what is its acceleration?
(How quickly does it slow down?)

A2.  Use  F = m x a
or  a = F ÷ m

    a = 1500 ÷ 1500
= 1 m/s2.

After we have doubled the mass of the car and
applied the same force from the brakes,
the car is now slowing down at only half the rate.

The car with twice the mass will take twice as long to stop
(requiring twice the braking distance - see kinetic energy).

Notice that the rate of negative acceleration (slowing down)
only depends on the force of the brakes and the mass of the car,
not how fast the car is going.
A faster moving car will take further to stop for the same acceleration
(the same rate of slowing down, see the previous page).

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