Speed and acceleration

1 of 46 © Boardworks Ltd 2007



What is speed?

Speed is a measure of how far an object moves in a given time.

This jet is travelling at350 m/s. This means the jet travels 350 metres every second.

This car is travelling at 60

mph. This means the car travels 60 miles every hour.


The speed of an object does not depend on the direction in which it is travelling. The velocity of an object is the speed and direction in which it is moving.

The car is travelling north with a velocity of 10 m/s.

How is velocity different to speed?

As the car goes round the corner, the speed of the car remains constant but the velocity changes.


How is speed calculated?

The speed of an object can be calculated using this equation:

distance travelled time taken

speed =

Speed is measured in metres per second (m/s).

Distance travelled is measured in metres (m).

Time taken is measured in seconds (s).

The standard unit for speed in physics is m/s, but other units such as kilometres per hour (km/h) are more convenient when measuring the speed of vehicles. Why is this?


Calculating speed question

A train takes 100 seconds to travel 1,500 m. What is the speed of the train?

= 15 m/s

speed =distance

time

= 1,500 100


Using a formula triangle

A formula triangle helps you to rearrange a formula. The formula triangle for speed (s), distance (d) and time (t) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find speed (s), cover up s…

…which gives the formula…

s =dt


Calculating speed question

A car travels at 25 m/s for 3 minutes. How far does it travel?

= 4,500 m = 4.5 km

speed =distance

time

= 25 x 180

distance = speed x time


Speed, distance, time calculations



Representing speed


Analyzing distance–time graphs


Calculating speed from the gradient

The slope of a graph is called the gradient.

The gradient of the line in adistance–time graph equals the speed.

It is difficult to calculate the gradient of ‘realistic’ graphs because the line is curved.

Simple graphs use straight lines only, making it easy to calculate the gradient.

time

dist

ance

time

dist

ance


What’s the speed?

What is the speed of the object between points A and B?

time (s)

dist

ance

(m)

0 21 3 4 5 6 7 8 90

10203040506070

A

B the object has moved

60 m (70 - 10 )

it took 3 s to move this distance (6 - 3)

speed = distance/time

= 60/3

= 20 m/s


Calculating speed from graphs


DIY distance–time graph



The acceleration of an object is a measure of how quickly its velocity changes.

A train accelerates in a straight line from rest. As it does, its velocity increases.

The brakes on this motorcycle are causing it to slow down. This is negative acceleration or deceleration.

What is acceleration?


The acceleration of an object can be calculated using this equation:

change in speedtime taken

acceleration =

Acceleration is measured in metres per second per second (m/s2).

Change in speed is measured in metres per second (m/s).

Time taken is measured in seconds (s).

How is acceleration calculated?


A racing car accelerates from rest to a speed of 60 m/s in a time of 4 seconds. What is the acceleration of the car?

= 15 m/s2

change in speedtime taken

acceleration =

= 604

Acceleration problem


Using a formula triangle

A formula triangle helps you to rearrange a formula. The formula triangle for acceleration (a), speed (s) and time (t) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find acceleration (a), cover up a…

…which gives the formula…

a =st


A hungry cheetah spots a gazelle and decides to chase it. The cheetah accelerates at 10 m/s2 from rest until it reaches 20 m/s. How long did this take?

acceleration = change in speedtime taken

= 2010

= 2 s

Acceleration problem

time taken = change in speedacceleration


Acceleration problems calculations



Analyzing speed–time graphs


Calculating acceleration from the gradient

This gradient of the line in a speed–time graph represents acceleration

How can the acceleration of an object be calculated from a speed–time graph?

If the gradient goes up, the object has a positive acceleration.

If the gradient goes down, the object has a negative acceleration, or deceleration.

timesp

eed

time

spee

d


What’s the acceleration?

What is the acceleration of the object between points A and B?

time (s)

spee

d (m

/s)

0 21 3 4 5 6 7 805

101520253035

A

B the object’s speed has

increased by 20 m/s (25 - 5)

it took 4 s to change speed (6 - 2)

acceleration = speed/time

= 20/4

= 5 m/s2


Calculating acceleration from graphs


The area under a speed–time graph


DIY speed–time graph



Speed and safety

Why are speed limits important?


Why have speed limits?

Speed limits are an important part of road safety. They aim to prevent drivers from driving at speeds that are unsuitable and unsafe.

The speed limit of a particularroad depends on a range offactors, such as how straight or curved it is, and its location.

The faster a vehicle is driving, the longer it will take to stop – the overall distance this takes is the stopping distance.

stopping distance = thinking distance + braking distance


Stopping distances


alcohol

other drugs and some medicines

tirednessdistractions, such as

mobile phonesspeed

What affects thinking distance?

The thinking distance is the distance a vehicle travels in the time it takes for a driver to react to a situation and apply the brakes.

What factors will affect thinking distance?


weather

condition of tyres/brakes

What affects braking distance?

The braking distance is the distance a vehicle takes to stop once the driver has applied the brakes.

What factors will affect braking distance?

condition of roadspeed


Factors affecting stopping distances


How do speed cameras work?

There are several types of speed camera., They use different methods to calculate the speed of a vehicle.

Gatso speed cameras use radar to detect the speed of a vehicle, then take two photos (half a second apart) to provide visual evidence. Lines marked on the road indicate how far the vehicle has travelled in that time.

Truvelo speed cameras are activated by pressure detector cables in the road. The cables are 10 cm apart and a computer calculates how long it takes the vehicle to pass from one to another, and therefore the speed of the vehicle.


Speeding and speed cameras



Glossary (1/2)

acceleration – A measure of how an object’s velocity changes over time. It usually refers to an object that is speeding up.

braking distance – The distance it takes for a vehicle to stop once its brakes have been applied.

deceleration – Negative acceleration, i.e. slowing down.

non-uniform – Speed or acceleration that is constantly changing.

speed – A measure of how far an object moves in a given time.


Glossary (2/2)

stopping distance – The total distance it takes for a vehicle to stop, i.e. thinking distance plus braking distance.

thinking distance – The distance it takes for a driver to react to a situation and apply the brakes.

uniform – Speed or acceleration that is constant and unchanging.

velocity – A measure of the speed and direction of a moving object.


Anagrams


What does the graph show?


What does the graph show?


Multiple-choice quiz

Date post:	16-Jan-2017
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Speed and acceleration

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