2.1 Distance, Speed And Acceleration

State the equation linking distance, speed and time. Give appropriate units.

Speed\= distance/time

Speed (m/s), distance (m), time (s)

How can speed be calculated from a distance-time graph?

The speed is equal to the gradient of the graph.

How do you calculate the gradient of a line?

m\= Δy/Δx

What must be done to calculate speed at a given time from a distance-time graph for an accelerating object?

● Drawing a tangent to the curve at the required time
● Calculating the gradient of the tangent.

Define acceleration.

The increase in speed over a certain period of time.

Define deceleration.

The decrease in speed over a certain period of time.

State the equation for the average acceleration of an object. Give appropriate units.

Acceleration \= Change in Velocity/Time taken

Acceleration (m/s^2), velocity (m/s), time (s)

How do you calculate the change in velocity?

Δv\= v-u

v\= Final velocity.
u\= Start velocity.

Another word for velocity is...

Speed.

What does the gradient of a velocity-time graph represent?

Acceleration.

How can the distance travelled by an object be calculated from a velocity-time graph? (Higher)

The distance travelled is equal to the area under the graph.

State one similarity and one difference between speed and velocity.

Similarity- They both have magnitude.
Difference- Velocity has a specific direction whilst speed doesn't.

Describe the motion at points A, B and C (QER style question).

At point A, velocity increases from 0 m/s to 40 m/s in 20 seconds. This shows a constant acceleration of 2 m/s².

At point B, it travels at a constant velocity of 40 m/s for 30 seconds. Here, there is no acceleration.

At point C, velocity increases from 40 m/s to 80 m/s in 10 seconds. This shows a constant acceleration of 4 m/s².

What is thinking distance?

The distance traveled by the vehicle in the time it takes the driver to react.

What is braking distance?

The distance traveled by the vehicle in the time the brakes act.

What is the stopping distance of a vehicle equal to?

The sum of thinking distance and braking distance.

Overall stopping distance \= thinking + braking distance.

For a given braking distance, if the vehicle's speed is increased, what can be said about its stopping distance?

The stopping distance is increased with an increase in speed.

How does the speed of the vehicle affect braking and thinking distance?

Both thinking and braking (and hence overall stopping) distances are increased when the speed is increased (as more distance is travelled in the same reaction time, or under the same braking force).

Give a typical range of values for human reaction time.

- 0.2 seconds- 0.9 seconds
- It is approximately 0.6 seconds.

Give factors which can affect a driver's reaction time (thinking distance).

1. Tiredness
2. Distractions (i.e. drugs, alcohol)
3. Poor visibility
4. Speed of vehicle

Give factors which may affect braking distance.

1. Adverse (wet/icy) road conditions
2. Poor tire/brake conditions
3. Speed of vehicle
4. How heavy loaded the vehicle is

What factor affects both thinking and braking distance?

Speed.

How do you calculate the thinking distance?

Thinking distance \= speed x reaction time

What does the gradient of a thinking distance (x) - speed (y) graph represent?

m\= reaction time.
Reaction time is constant (0.6 seconds) therefore the graph is directly proportional.
D/S\= t