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

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

Determine:

(a) The braking distance of the car

(b) The driver's reaction time

Answer:

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

The thinking and stopping distance definitions are often confused with each other. Remember that the thinking distance is to do with the driver whilst the stopping distance is to do with the vehicle and road conditions

The graph below shows how the thinking distance of a driver depends on the speed of the car.

(a) Describe the connection between thinking distance and speed.

(b) Some people drive when they are tired, despite warnings against doing so. Draw a new line on the graph to show how thinking distance varies with speed for a tired driver.

Answer:

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:

A passenger travels in a car at a moderate speed. The vehicle is involved in a collision, which brings the car (and the passenger) to a halt in 0.1 seconds. Estimate:

a) The acceleration of the car (and the passenger)

b) The force on the passenger

Answer:

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

Remember that resultant force is a vector quantity. Examiners may ask you to comment on why its value is negative - this happens when the resultant force acts in the opposite direction to the object's motion.

In the worked example above, the resultant force opposes the passenger's motion, slowing them down (decelerating them) to a halt, this is why it has a minus symbol.