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Thinking, Braking & Stopping Distances | Physics for Grade 10 PDF Download

Thinking & Braking Distances

  • The stopping distance of a car is defined as:
    • The total distance travelled during the time it takes for a car to stop in response to some emergency
  • It can be written as an equation involving two distances:
    Stopping distance = Thinking distance + Braking distance
  • Where:
    • Thinking distance = the distance travelled in the time it takes the driver to react (reaction time) in metres (m)
    • Braking distance = the distance travelled under the braking force in metres (m)
    • Stopping distance = the sum of the thinking distance and braking distance, in metres (m)
  • For a given braking force, the greater the speed of the vehicle, the greater the stopping distance

Question for Thinking, Braking & Stopping Distances
Try yourself:At a speed of 20 m/s, a particular vehicle had a stopping distance of 40 metres. The car travelled 14 metres whilst the driver was reacting to the incident in front of him. What was the braking distance?
View Solution

Estimating Stopping Distances

  • For a given braking force, the speed of a vehicle determines the size of the stopping distance
    • The greater the speed of the vehicle, the larger the stopping distance
  • The image below shows how the stopping distance of a typical family car increases with increasing speed:
    A vehicle`s stopping distance increases with speed. At a speed of 20 mph the stopping distance is 12 m, whereas at 60 mph the stopping distance is 73 m (reproduced from the UK Highway Code)
    A vehicle's stopping distance increases with speed. At a speed of 20 mph the stopping distance is 12 m, whereas at 60 mph the stopping distance is 73 m (reproduced from the UK Highway Code)

Thinking, Braking & Stopping Distances | Physics for Grade 10

Graphs Relating Speed to Stopping Distance

  • The velocity-time graph below shows how the velocity of a car will typically change during an emergency stop
    Graph showing how the velocity typically changes as a vehicle comes to an emergency stop
    Graph showing how the velocity typically changes as a vehicle comes to an emergency stop
  • While the driver reacts (the time taken to press the brakes is called the reaction time), the vehicle continues moving at a constant velocity
    • The area underneath the graph during this time represents the thinking distance
  • As soon as the brakes are applied, the vehicle decelerates to a halt
    • The area underneath the graph during this time represents the braking distance

Solved Example

Example: While driving at a speed of 35 m/s, Stephen sees an obstacle in the road at time t = 0.The velocity-time graph below shows how the speed of the car changes as Stephen reacts and slams the brakes, bringing the car to a halt.

Thinking, Braking & Stopping Distances | Physics for Grade 10
Determine
(a) The braking distance of the car.
(b) The driver's reaction time.

Part (a)
Step 1: Identify the section of the graph which represents the braking distance
(i) The area under a velocity-time graph represents distance travelled
(ii) The braking distance of the car is the distance travelled under the braking force
(iii) This area of the graph is shaded below:
Thinking, Braking & Stopping Distances | Physics for Grade 10

Step 2: Calculate the area under the graph during the car's deceleration
The area is a triangle, so the braking distance is given by:
Braking distance = Area = ½ × base × height
Braking distance = ½ × (4.5 – 1) × 35 = 61.3 m

Part (b)
Step 1: Determine how long the driver takes before the brakes are applied

Between seeing the obstacle and applying the brakes, 1 second passes
This sequence of events is labelled on the graph below:
The driver`s reaction time is the time between the moment they see the obstacle to the moment the brakes are appliedThe driver's reaction time is the time between the moment they see the obstacle to the moment the brakes are applied

Therefore, the driver's reaction time is 1 s

Measuring Reaction Time

  • The reaction time is defined as:
    A measure of how much time passes between seeing something and reacting to it
  • The human reaction time for someone who is alert - i.e. someone waiting to react to something happening, like an athlete waiting for the start of a race - is usually in the range of 0.2 - 0.9 seconds
  • A simple method for measuring human reaction time is illustrated below:
    Thinking, Braking & Stopping Distances | Physics for Grade 10

Thinking, Braking & Stopping Distances | Physics for Grade 10

  • Person A holds a 30 cm ruler vertically, such that the bottom end of the ruler hovers over the top of the hand of Person B
  • Person A should release the ruler unexpectedly
  • As soon as Person B sees the ruler move, they should close their hand, catching it
  • The ruler is marked at the point at which it was caught by Person B - i.e. in line with the top of their hand
  • This gives a measurement of the distance the ruler fell
    • The greater the distance, the longer the reaction time

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