5.4 Braking and collisions

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• Middelbare school
• havo, vwo
• Leerjaar 2

5.4 Braking and collisions

In traffic you always have to able to stop in time without having a collision.

What factors will influence the braking distance?

1. Mass of the car
2. Braking force
3. Speed of the car
4. All answers above

The higher the initial speed,
the longer the braking distance.

The greater the mass of the vehicle,
the longer the breaking distance.

If the road is slippery you have to brake slowly, othewise the car will slip.

Braking distance

Depends on:

• Initial speed;
  the faster you are going, the greater the braking distance
  
• Total mass;
  the greater the mass the greater the braking distance
  
• Braking force;
  the harder the brakes are pressed the shorter the braking distance

Stopping distance = reaction distance + braking distance

Reaction distance

Reaction distance  =  reaction time  x  velocity

The reaction time in normal conditions is around 1.0 second.

Braking distance

Reaction distance

A horse runs to the finishline at 39.6 km/h. The drivers reaction time is 0.2 s. The braking distance is 22.8 m. Determine the stopping distance.

Formulas:
stopping distance = reaction distance + braking distance

reaction distance = reaction time x velocity

A horse runs to the finishline at 39.6 km/h. The drivers reaction time is 0.2 s. The braking distance is 22.8 m. Determine the stopping distance.

  v = 39.6 km/h = 11 m/s (39.6 / 3.6)

  t = 0.2 s (reaction time)

  braking distance = 22.8m 

stopping distance = reaction distance + braking distance

reaction distance = v x t = 11 x 0.2 = 2.2 m

           stopping distance = reaction distance + braking distance
           stopping distance = 22.8 + 2.2 = 25m

initial speed and braking distance

If the speed is n times bigger, 

the braking distance becomes n² times longer.

v = 10 m/s

s = 5 m

v = 20 m/s

s = 20 m

v = 30 m/s

s = 45 m

n² = 2² = 4

braking distance = 4 * 5 = 20 m

n² = 3² = 9
braking distance = 9 * 5 = 45 m

If the initial velocity is 10 m/s the braking distance is 5 m. What is the braking distance with an initial velocity of 90 km/h?

If the initial velocity is 10 m/s the braking distance is 5 m. What is the braking distance with an initial velocity of 90 km/h?

v = 90 km/h = (90/3.6) m/s = 25 m/s

n = 25/10 = 2.5
n² = 2.5² = 6.25
braking distance = n² x old braking distance 
braking distance = 6.25 x 5
braking distance = 31.25 m

If the initial velocity is 10 m/s the braking distance is 5 m. What is the initial velocity with a braking distance of 80 m?

If the initial velocity is 10 m/s the braking distance is 5 m. What is the initial velocity with a braking distance of 80 m?

braking distance = 80 m

braking distance = n² x old braking distance 
80 = n² x 5
n² = 80 / 5 = 16
n = √16 = 4
initial velocity = 4 * 10 = 40 m/s

Homework

finish chapter 5