Vectors and Equations of Motion (suvat) P5b(ii) You will find out about: How to use equations of motion

Average Speed

Equations of Motion When an object accelerates in a straight line the equations of motion are used to find out more about how it moves. You need to remember ‘suvat’: s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s REMEMBER: It is very easy to confuse u and v. v and f (for final…) start with the same sound

Equation 1 s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s

Equation 2 The next equation you need to know is: Final speed = initial speed + (acceleration x time) or v = u + at s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s Example Question: An aeroplane moving at 60m/s starts to accelerate uniformly at 12m/s 2. How fast is it moving after 20 seconds? Again use ‘suvat’ and input the numbers: s = do not know u = 60m/s v = need to work out a = 12m/s 2 t = 20s It does not matter that we do not know s as Equation 2 does not use it: v = u + at v = 60 + (12x20) v = 300m/s

A little more about Equations 1 and 2 This is Equation 1 This is Equation 2 Practice re-arranging these equations so you can show how to derive them in the form they are shown in the exam paper.

Difficult Questions using Equations 1 and 2 Difficult Question 1: A bullet reached a speed of 400m/s after accelerating uniformly at 20,000m/s 2 for second. How fast was it going before accelerating? Using ‘suvat’: s = do not know u = need to find out v = 400 m/s a = 20,000 m/s 2 t = s We cannot use equation 1 as we do not know s. We can however, use equation 2: v = u + at This is more difficult because we need to work out u rather than v. Most students find it easier to re-arrange the equation at the end: v = u + at plug numbers in: 400 = u + (20,000 x 0.001) 400 = u + 20 now we can re-arrange : 400 – 20 = u 380 m/s = u s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s If your math is good you could re-arrange the equation from the start so that: u = v - at BUT if you make a mistake here you will get the wrong answer!

More equations of motion for uniform acceleration! and we know that Equation 2 is: v = u + at You can see that v is now swapped for u+at THIS IS EQUATION 3! and we know that Equation 2 is: v = u + at THIS IS EQUATION 4!

Re-cap of Equations s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s If we know three of the ‘suvat’ quantities then we can find out the other two using the four Equations.

Taking stock… s = distance travelled, m u = initial velocity, m/s v = final velocity, m/s a = acceleration, m/s 2 t = time, s Question: Usain Bolt reaches a speed of m/s from rest after running 45 m. Find his acceleration. Using ‘suvat’: s = 45 m u = 0 m/s v = m/s a = need to work out t = do not know Let us look at the four Equations to determine which we can use: no, because we do not know t no, because we do not know t and does not use s no, because we do not know t yes!! Which Equation shall we use?

Does Gravity play a part? In a word, yes! If we ignore air resistance all objects accelerate towards the Earth at 10m/s 2 due to gravity. But an object going upwards decelerates at 10m/s 2. As it is going in the opposite direction to the Earth its acceleration is -10m/s 2 and at its highest point its velocity, v, would be 0m/s. This trampolinist jumping upward is moving in the opposite direction of the Earth. Therefore their acceleration is -10m/s 2. When they reach their highest point v will be 0m/s. On their way back down, and moving in the direction towards Earth, their acceleration will be 10m/s 2. Question: This trampolinist jumped a second time vertically upward at 12.5m/s. How high did they go? Using ‘suvat’: s= need to find out u = 12.5 m/s v = 0 m/s a = -10 m/s 2 t = do not know Which Equation shall we use? No because we do not know t No, because we want to find out s and we also do not know t No because we do not know t yes!!

Questions 1.Give two reasons why a speed of a lorry may change during its trip to a warehouse. 2.A cyclist started cycling a bike with an acceleration of 3.5m/s 2. How fast was it going after 20 seconds? Is this possible? 3.A Ferrari accelerated at 8m/s 2 for 6 seconds reaching a top speed of 345 km/h. How fast was it moving before accelerating in m/s? How far did it travel? 4.A cannonball was dropped from a chalk pit that was 120 metres high. With what speed did it hit the ground below?

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