SUVAT equations Monday, 14 March 2016 - PowerPoint Presentation

SUVAT equations Monday, 14 March 2016 A car drives with a constant speed of 84 miles per hour. How long will it take to travel a distance of 140 miles?A train travels with a constant speed of 36 miles per hour. How far can it travel in 1 hour 30 minutes?Juan roller skates 42 miles in 210 minutes. What is his average speed in miles per hour?Julia roller skates 9 miles with a constant speed of 18 mph and another 19 miles with a constant speed of 12 mph. How much time in total does she take to travel these distances?Noah rides his motorcycle 65 km with a constant speed of 60 km/h and another 204 km with a constant speed of 72 km/h. What is his average speed for the total trip? 1 hour 40 minutes 1 hour 30 minutes 12 miles per hour 2 hours and 5 minutes 68.7 km/h

SUVAT equations s = distance u = initial velocity (speed)v = final velocity (speed)a = accelerationt = timeThere is an equation for every scenario – you only need to know 3 facts to find out either of the other two.LO: Learn to use SUVAT equationsSuccess looks like: Recognising which equation to use and manipulating your equation of choice

SUVAT equations It is important to write this very formally. You should always read the question first and pick out all of the information you’ve been given. ExampleUsain Bolt runs the 100m in 9.58s. If he starts at 0 m/s and accelerates uniformly (at the same rate) how fast will he be travelling when he crosses the finish line?

If I have the initial velocity , acceleration and distance, and I want to find out the time taken, what equation will I use?v = u + atv2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

If I have the time , acceleration and distance, and I want to find out the initial velocity taken, what equation will I use?v = u + atv2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

If I have the time , final velocity and distance, and I want to find out the initial velocity taken, what equation will I use?v = u + atv2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

If I have the time , acceleration and initial velocity, and I want to find out the final velocity taken, what equation will I use?v = u + atv2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

If I have the final velocity , acceleration and distance, and I want to find out the time taken, what equation will I use?v = u + atv2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

If I have the final velocity , acceleration and distance, and I want to find out the time taken, what equation will I use?In fact this is a mini-test – you can still find the time taken but you have to take an extra step. Using v, a and s, find u, then any of the equations can be used to find t.v = u + atv 2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t Start with me!

SUVAT equations Monday, 14 March 2016 A typical Fiat 500 has a 0 – 60 mph time of 11.6 seconds.How far has it travelled in that time?Which equation will you use? v = u + at v 2 = u2 + 2as s = ut + ½at 2 s = ½(u + v)t 0 mph = 0 mile per second 60 mph = 1/60 mile per second

0.0216 miles34.76 metres SUVAT equationsMonday, 14 March 2016The fastest model of the Audi R8 has a 0 - 60mph time of 2.6 seconds.How far has it travelled in that time? Compare its distance with the Fiat 500’s.Convert your answer into metres,1 mile = 1609 metres. 0 mph = 0 mile per second60 mph = 1/60 mile per second v = u + at v 2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t

SUVAT equations Monday, 14 March 2016 We can also use an equation to find out how quickly it accelerated.A typical Fiat 500 has a 0 - 60mph time of 11.6 seconds.v = u + at v 2 = u2 + 2as s = ut + ½at 2 s = ½(u + v)t 0 mph = 0 mile per second 60 mph = 1/60 mile per second

SUVAT equations Monday, 14 March 2016 We can also use an equation to find out how quickly it accelerated.A typical Fiat 500 has a 0 - 60mph time of 11.6 seconds.v = u + atThis will need to be rearranged…a = v - ut a = (v – u) ÷ t a = (u – v) ÷ t a = t ÷ (v – u) 0 mph = 0 mile per second 60 mph = 1/60 mile per second

SUVAT equations Monday, 14 March 2016 The fastest model of the Audi R8 has a 0 - 60mph time of 2.6 seconds.What was its average acceleration?0 mph = 0 mile per second60 mph = 1/60 mile per secondv = u + at v 2 = u2 + 2as s = ut + ½at 2 s = ½(u + v)t

SUVAT equations Monday, 14 March 2016 The quickest model of the Ferrari 458 completes a quarter mile in 10.7 seconds. Calculate it’s final velocity. v = u + atv2 = u2 + 2as s = ut + ½at 2 s = ½(u + v)t 0 mph = 0 mile per second 60 mph = 1/60 mile per second

SUVAT equations Monday, 14 March 2016 A Bugatti Veyron takes 10.0 seconds to complete a quarter mile. Find its acceleration. v = u + at v2 = u 2 + 2as s = ut + ½at 2 s = ½(u + v)t 0 mph = 0 mile per second 60 mph = 1/60 mile per second A McLaren P1’s final velocity in a quarter mile is 152mph. Calculate its time. 0.0033hrs 11.8s 0.0033hrs 11.8s Got the McLaren’s time wrong? Start on Lemon & Herb. Got the McLaren’s time right but not the Bugatti? Start on Medium. Got the McLaren and the Bugatti’s info right? Start on HOT!

Lemon & Herb A car accelerates uniformly from 5m/s to 15m/s taking 7.5 seconds. How far did it travel during this period. A runner starts from rest, runs for 30 seconds at a uniform acceleration of 2m/s2, how fast are they travelling at the end?A car accelerates uniformly at a rate of 3m/s2 for 20 seconds from rest. How far has it travelled? A formula 1 car is travelling at 15m/s before it accelerates uniformly to 30m/s over 20s. How far has it travelled? Medium A train starts from rest and accelerates uniformly at 1.5m/s 2 until it attains a speed of 30m/s. Find the time taken and the distance travelled . In travelling the 70cm along a rifle barrel, a bullet uniformly accelerates from rest to a velocity of 210m/s. Find the acceleration involved and the time taken for which the bullet is in the barrel. A particle is accelerated from 1m/s to 5m/s over a distance of 15m. Find the acceleration and the time taken . A car accelerates uniformly from rest and after 12 seconds has covered 40m. What are its acceleration and its final velocity ? A car is being driven along a road at 25m/s when the driver suddenly notices that there is a fallen tree blocking the road 65m ahead. The driver immediately applies the brakes giving the car a constant retardation of 5m/s 2 . How far in front of the tree does the car come to rest ? HOT Initial velocity 5m/s, final velocity 36km/hr, acceleration 1.25m/s/s. Distance ? A train is uniformly slowed down from 35m/s to 21m/s over a distance of 350m. Calculate the acceleration and the time taken to come to rest from the 35m/s.   A particle moves with uniform acceleration 0.5m/s 2 in a horizontal line ABC. The speed of the particle at C is 80m/s and the times taken from A to B and from B to C are 40 and 30 seconds respectively. Calculate (a) Speed at A (b) Distance BC EXTRA HOT A train travels along a straight piece of track between 2 stations A and B. The train starts from rest at A and accelerates at 1.25m/s 2 until it reaches a speed of 20m/s. It then travels at this speed for a distance of 1560m and then decelerates at 2m/s 2 to come to rest at B. Find Distance from A to B ( b) Total time taken for the journey ( c) Average speed for the journey

Lemon & Herb A car accelerates uniformly from 5m/s to 15m/s taking 7.5 seconds. How far did it travel during this period. 75mA runner starts from rest, runs for 30 seconds at a uniform acceleration of 2m/s2, how fast are they travelling at the end?60m/sA car accelerates uniformly at a rate of 15m/s2 for 20 seconds from rest. How far has it travelled? 600m A formula 1 car is travelling at 15m/s before it accelerates uniformly to 30m/s over 20s. How far has it travelled?450m Medium A train starts from rest and accelerates uniformly at 1.5m/s 2 until it attains a speed of 30m/s. Find the time taken and the distance travelled . 20s 300m In travelling the 70cm along a rifle barrel, a bullet uniformly accelerates from rest to a velocity of 210m/s. Find the acceleration involved and the time taken for which the bullet is in the barrel. 31500 ms -2 0.0067 secs A particle is accelerated from 1m/s to 5m/s over a distance of 15m. Find the acceleration and the time taken . 5 secs 0.8 ms -2 A car accelerates uniformly from rest and after 12 seconds has covered 40m. What are its acceleration and its final velocity ? 0.55 ms -2 6.67 ms -1 A car is being driven along a road at 25m/s when the driver suddenly notices that there is a fallen tree blocking the road 65m ahead. The driver immediately applies the brakes giving the car a constant retardation of 5m/s 2 . How far in front of the tree does the car come to rest ? 2.5m before the tree HOT Initial velocity 5m/s, final velocity 36km/hr, acceleration 1.25m/s/s. Distance ? 30m A train is uniformly slowed down from 35m/s to 21m/s over a distance of 350m. Calculate the acceleration and the time taken to come to rest from the 35m/s.  -1.12 ms -2 , 31.25 secs A particle moves with uniform acceleration 0.5m/s 2 in a horizontal line ABC. The speed of the particle at C is 80m/s and the times taken from A to B and from B to C are 40 and 30 seconds respectively. Calculate (a) Speed at A (b) Distance BC a) 45 ms -1 b) 2175m EXTRA HOT A train travels along a straight piece of track between 2 stations A and B. The train starts from rest at A and accelerates at 1.25m/s 2 until it reaches a speed of 20m/s. It then travels at this speed for a distance of 1560m and then decelerates at 2m/s 2 to come to rest at B. Find ( a) Distance from A to B 1820m ( b) Total time taken for the journey 104 seconds ( c) Average speed for the journey 17.5ms -1

Write a note to remind yourself of the different stages of using the SUVAT equations. What should your future self do first? Write any errors you keep making that you should avoid in the future.Final Velocity Initial Velocity Space Time Acceleration Constant Uniform