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Forces and Motion

The Stopping Distance of a Car - Velocity.

The total stopping distance = thinking distance + braking distance.

Both the thinking distance and the braking distance
are changed as the velocity of a car changes.

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

How does Velocity affect the Braking Distance of a Car?

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

Q1
.  A car is moving with a velocity (speed) of 10 m/s.
When the brakes are applied the car slows down
and has a constant negative acceleration  of -2 m/s2.
What is its braking distance?

A1.  Find how much time the car took to stop.
Then find the average velocity of the car.
Then calculate the braking distance.

Use   a = (v-u) ÷ t
to find the time (
t) for how long it takes the car to stop.

a = - 2
v =
u = 10

t = (v-u) ÷ a
t = (0 - 10) ÷ -2
t = 10 ÷ 2

t = 5 seconds.

For an object that has a constant acceleration,
the average velocity = (initial velocity + final velocity) ÷ 2
= (10 + 0) ÷ 2
= 5 m/s.

As velocity = distance ÷ time
then distance = velocity x time

The braking distance of the car
= 5 x 5
= 25 m.

Q2
.  The same car is now moving with twice the velocity at 20 m/s.
When the brakes are applied,
the car has the same constant negative acceleration of -2 m/s2.
What is its braking distance?

A2.  Use the same method as above, a = (v-u) ÷ t

a = -2
v =
u = 20

t = (v-u) ÷ a

t = (0 - 20) ÷ -2
t = 20 ÷ 2

t = 10 seconds.

The average velocity = (initial velocity + final velocity) ÷ 2
= (20 + 0) ÷
= 10 m/s.

Since velocity = distance ÷ time
distance = velocity x time

The braking distance of the car
= 10 x 10
= 100 m.

Notice that doubling the velocity of the car from 10 to 20 m/s
has more than doubled the braking distance.
In fact the braking distance goes up x4 when the velocity goes up x2.
This is because of
the effect of velocity on the kinetic energy of the car
.

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