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**P3b(ii) Changing Speed You will learn about: Acceleration**

P3b(ii) Changing Speed You will learn about: Acceleration How Acceleration, Speed and Time are linked Velocity and Relative Velocity

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**Acceleration www.PhysicsGCSE.co.uk**

This table shows that the speed of a car increases by a constant amount – 10m/s in this case. At 1 second the car was travelling at 10 m/s. At 2 seconds the car was no longer travelling at 10 m/s but increased to 20 m/s. And at 3 seconds you can see that the speed has increased yet again to 30 m/s. For each second that passes the car increases its speed by 10 m/s. When an object changes its speed it is accelerating. Recall that the unit for acceleration is m/s2 . For each second that passes the speed increases by 10 m/s. So 10 m/s change per second. This can be written as 10 m/s/s or 10 m/s2. Time / s Speed / m/s 1 10 2 20 3 30 4 40 Time / s Speed / m/s 40 1 30 2 20 3 10 4 This time the table shows deceleration or negative acceleration

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**Acceleration calculation**

Acceleration calculation To calculate acceleration you need to use: Acceleration = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑝𝑒𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 A golfer hits a golf ball. It increases in speed by 30m/s in 4 seconds. So to calculate its acceleration: Acceleration = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑝𝑒𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 Acceleration = 30 𝑚/𝑠 4 𝑠 Acceleration = 7.5 m/s2

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**Velocity www.PhysicsGCSE.co.uk**

To understand the difference between speed and velocity you need to understand what scalars and vectors are. We ask Bumblebee to scoot off at 2 m/s. He scoots off. But we didn’t tell him which way to go! Therefore we told him the amount (or magnitude) but not the direction to go in. The information we gave him only has one piece of information. This is called a scalar and speed is an example. If we asked Bumblebee to scoot off at 2 m/s headed due North then we would have provided Bumblebee with a magnitude AND direction. Therefore we have provided TWO pieces of information. This is a vector and velocity is an example. Easy to remember: S for Scalar and S for Speed. V for Vector and V for Velocity. Acceleration can be written as +2m/s2 or -2m/s2. The + or – sign tells us the direction (forwards or backwards) and the number is the magnitude. Therefore acceleration is a Vector. So Bumblee has a speed of 2m/s but has a velocity of 2m/s due North…

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**Relative Velocity www.PhysicsGCSE.co.uk Car A +40m/s Car B +40m/s**

This time the two cars are moving at the SAME Velocity side by side. If you were in one car then the other car would not be going any faster or slower than you… it appears to not be moving! Using the same formula: Car A has a velocity of +40m/s Car B has the same velocity of +40m/s as it is moving in the same direction. The Velocity of Car A relative to Car B = (+40m/s)-(+40m/s) = 0m/s Car A moves right at 40m/s. Car B moves to the left at 40 m/s. This means that their velocities are in opposite directions. So Car A has a velocity of +40m/s and Car B has a velocity of -40m/s. To calculate the RELATIVE VELOCITY you need to take one velocity away from the other: The velocity of Car A relative to Car B = (+40m/s) – (-40m/s) = +80m/s The velocity of Car B relative to Car A = (-40m/s) – (+40m/s) = -80m/s This makes sense… if you were in Car A then Car B would seem to be moving twice as fast toward you because you are moving toward it and it is moving toward you.

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**Relative Velocity Rules**

Relative Velocity Rules The boxes represent vehicles and the arrows depict their velocities Car A Car B Relative Velocity Calculations Car A relative to Car B = (+30m/s) – (-70m/s) = +100m/s Car B relative to Car A = (-70m/s) – (+30m/s) = -100m/s Car A relative to Car B = (+20m/s) – (+20m/s) = 0m/s Car B relative to Car A = (+20m/s) – (+20m/s) = 0m/s Car A relative to Car B = (+10m/s) – (-10m/s) = +20m/s Car B relative to Car A = (-10m/s) – (+10m/s) = -20m/s 30m/s 70m/s 20m/s 10m/s Simple Rules: If two vehicles are moving in opposite directions then their relative velocities are the sum of each other’s velocities. Vehicle A will have a + sign. Vehicle B will have a – sign. If two vehicles are moving at the same direction at the same velocity then their relative velocity will equal 0m/s

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**Acceleration but the speed is constant?**

Acceleration but the speed is constant? A car maintains a steady constant 30 miles/h speed around a roundabout. The car is accelerating… but how? Recall that acceleration is a VECTOR. A vector comprises of a magnitude AND a direction. As long as ONE of these changes then the car will accelerate. So what is changing? The speed is constant so it is the DIRECTION that is constantly changing. The car is not going in a straight line but a curve. This means that the car IS accelerating even though the speed is constant. It is the same for any object that spins… REMEMBER that Acceleration = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 so if either changes then acceleration changes. Remember how to re-arrange this equation using the triangle rule.

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Questions A car accelerates from 0m/s to 40m/s in 8 seconds. Another car accelerates from 0m/s to 25m/s in 5 seconds. Which car has the greatest acceleration? An aeroplane decreases its speed by 250m/s in 5 seconds. Calculate its acceleration. Two cyclists pedal head on. Cyclist A is pedalling at 15m/s and Cyclist B is pedalling at 12m/s. What is their relative speed? A motorbike has a maximum acceleration of 7m/s2. Calculate the time taken to reach a speed of 42m/s, if the motorbike started from a standstill.

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Questions A car accelerates from 0m/s to 40m/s in 8 seconds. Another car accelerates from 0m/s to 25m/s in 5 seconds. Which car has the greatest acceleration? Car 1 acceleration = 40 𝑚/𝑠 8 𝑠 = 5m/s Car 2 acceleration = 25𝑚/𝑠 5 𝑠 = 5m/s2 so equal acceleration An aeroplane decreases its speed by 250m/s in 5 seconds. Calculate its acceleration Acceleration = −250 𝑚/𝑠 5 𝑠 = -50m/s2. Two cyclists pedal head on. Cyclist A is pedalling at 15m/s and Cyclist B is pedalling at 12m/s. What is their relative speed? A relative to B = (+15m/s) – (-12m/s) = +27m/s B relative to A = (-12m/s) – (+15m/s) = -27m/s A motorbike has a maximum acceleration of 7m/s2. Calculate the time taken to reach a speed of 42m/s, if the motorbike started form a standstill. Need to re-arrange acceleration equation = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 so time taken is the subject: time taken = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 42 𝑚/𝑠 7 𝑚/𝑠2 = 6 seconds

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