Estimating Braking Distances, Speeds & Accelerations (OCR Gateway GCSE Physics)

• 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)

Velocity-Time Graphs for 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

• 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

Part (a)

Step 1: Identify the section of the graph which represents the braking distance

• • The area under a velocity-time graph represents distance travelled
  • The braking distance of the car is the distance travelled under the braking force

• • This area of the graph is shaded below:

The braking distance of the car is the area shaded because the car decelerates once the brakes are applied

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 applied

• • Therefore, the driver's reaction time is 1 s

Part (a)

Step 1: Check if the line is straight and if it goes through the origin

• • The graph shows a straight line through the origin
  • Therefore, the thinking distance is directly proportional to the speed of the car

Part (b)

Step 1: Recall the factors which affect the thinking distance

• • Three additional factors affect the thinking distance, because they affect human reaction time:
    • Tiredness
    • Distractions
    • Intoxication

  • Hence, a tired driver's reaction time is greater (i.e. it takes longer for them to react)

Step 2: Draw a line that shows greater thinking distance for the same speed

• • At the same speed, a tired driver's thinking distance will be greater than a driver who is alert
  • This means a line should be drawn with a steeper gradient, as shown below:

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 applied

• • Therefore, the driver's reaction time is 1 s

Part (a)

Step 1: Estimate the required quantities and list the known quantities

A moderate speed for a car is about 50 mph or 20 m/s

• • Initial velocity ~ 20 m/s
  • Final velocity = 0 m/s
  • Time, t = 0.1 s

Step 2: Calculate the change in velocity of the car (and the passenger)

change in velocity = Δv = final velocity − initial velocity

Δv = 0 − 20

Δv = −20 m/s

Step 3: Calculate the acceleration of the car (and the passenger) using the equation:

Step 4: Calculate the deceleration

a = −20 ÷ 0.1

a ~ −200 m/s²

Part (b)

Step 1: Estimate the required quantities and list the known quantities

An adult person has a mass of about 70 kg

• • Mass of the passenger, m ~ 70 kg
  • Acceleration, a = −200 m/s²

Step 2: State Newton's second law 

• • This question involves quantities of force, mass and acceleration, so the equation for Newton's second law is:

F = ma

Step 3: Calculate an estimate for the decelerating force

F = 70 × −200

F ~ −14 000 N