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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/s^{2}.

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 = 0

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/s^{2}.

What is its braking
distance?

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

a = -2

v = 0

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) ÷ 2

= 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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