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What is speed? Speed is a measure of how far an object moves in a given time. This car is travelling at 60 mph. This means the car travels 60 miles every hour. This jet is travelling at 350 m/s. This means the jet travels 350 metres every second. 3 of 46 © Boardworks Ltd 2007
How is velocity different to speed? 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. As the car goes round the corner, the speed of the car remains constant but the velocity changes. 4 of 46 © Boardworks Ltd 2007
How is speed calculated? The speed of an object can be calculated using this equation: distance travelled speed = time taken Distance travelled is measured in metres (m). Time taken is measured in seconds (s). Speed is measured in metres per second (m/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? 5 of 46 © Boardworks Ltd 2007
Calculating speed question A train takes 100 seconds to travel 1, 500 m. What is the speed of the train? distance speed = time = 1, 500 100 = 15 m/s 6 of 46 © Boardworks Ltd 2007
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. 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… x 7 of 46 …which gives the formula… s = d t © Boardworks Ltd 2007
Calculating speed question A car travels at 25 m/s for 3 minutes. How far does it travel? distance speed = time distance = speed x time = 25 x 180 = 4, 500 m = 4. 5 km 8 of 46 © Boardworks Ltd 2007
Speed, distance, time calculations 9 of 46 © Boardworks Ltd 2007
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Representing speed 11 of 46 © Boardworks Ltd 2007
Analyzing distance–time graphs 12 of 46 © Boardworks Ltd 2007
Calculating speed from the gradient The slope of a graph is called the gradient. 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. distance The gradient of the line in a distance–time graph equals the speed. time 13 of 46 time © Boardworks Ltd 2007
What’s the speed? distance (m) What is the speed of the object between points A and B? 70 60 50 40 30 20 10 0 B the object has moved 60 m (70 - 10 ) it took 3 s to move this distance (6 - 3) A speed = distance/time = 60/3 0 1 2 3 4 5 6 7 8 9 time (s) 14 of 46 = 20 m/s © Boardworks Ltd 2007
Calculating speed from graphs 15 of 46 © Boardworks Ltd 2007
DIY distance–time graph 16 of 46 © Boardworks Ltd 2007
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What is acceleration? 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. 18 of 46 © Boardworks Ltd 2007
How is acceleration calculated? The acceleration of an object can be calculated using this equation: change in speed acceleration = time taken Change in speed is measured in metres per second (m/s). Time taken is measured in seconds (s). Acceleration is measured in metres per second (m/s 2). 19 of 46 © Boardworks Ltd 2007
Acceleration problem 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? acceleration = = change in speed time taken 60 4 = 15 m/s 2 20 of 46 © Boardworks Ltd 2007
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. 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… x 21 of 46 …which gives the formula… a = s t © Boardworks Ltd 2007
Acceleration problem A hungry cheetah spots a gazelle and decides to chase it. The cheetah accelerates at 10 m/s 2 from rest until it reaches 20 m/s. How long did this take? change in speed acceleration = time taken = = change in speed acceleration 20 10 = 2 s 22 of 46 © Boardworks Ltd 2007
Acceleration problems calculations 23 of 46 © Boardworks Ltd 2007
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Analyzing speed–time graphs 25 of 46 © Boardworks Ltd 2007
Calculating acceleration from the gradient How can the acceleration of an object be calculated from a speed–time graph? time If the gradient goes up, the object has a positive acceleration. 26 of 46 speed This gradient of the line in a speed–time graph represents acceleration time If the gradient goes down, the object has a negative acceleration, or deceleration. © Boardworks Ltd 2007
What’s the acceleration? speed (m/s) What is the acceleration of the object between points A and B? 35 30 25 20 15 10 5 0 B the object’s speed has increased by 20 m/s (25 - 5) it took 4 s to change speed (6 - 2) A 0 1 2 3 4 5 6 7 8 time (s) 27 of 46 acceleration = speed/time = 20/4 = 5 m/s 2 © Boardworks Ltd 2007
Calculating acceleration from graphs 28 of 46 © Boardworks Ltd 2007
The area under a speed–time graph 29 of 46 © Boardworks Ltd 2007
DIY speed–time graph 30 of 46 © Boardworks Ltd 2007
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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. 32 of 46 © Boardworks Ltd 2007
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. 33 of 46 © Boardworks Ltd 2007
Anagrams 34 of 46 © Boardworks Ltd 2007
What does the graph show? 35 of 46 © Boardworks Ltd 2007
What does the graph show? 36 of 46 © Boardworks Ltd 2007
Multiple-choice quiz 37 of 46 © Boardworks Ltd 2007
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