Mechanics introduction Lesson for Yr 10/11

Professor Splash http://www.bbc.co.uk/news/world-europe-12773427 How high do you think he jumped from? Don’t try this at home … [Teachers: the answer is below the video – ensure it is not visible.]

Heat Maps Gareth Bale Luka Modric The two ‘heat maps’ show data about two players in the match between Bayern Munich and Real Madrid. What do they tell us? What don’t they tell us? Gareth Bale Luka Modric

Usain Bolt – London 2012 Olympics displacement (s) velocity (v) time (t) time (t)

Velocity-time graph displacement – letter is s time – letter is t velocity (v) displacement – letter is s time – letter is t velocity at a particular time – letter is v velocity at the start – letter is u acceleration – letter is a time (t)

Velocity-time graph displacement time velocity start velocity Velocity in m/s displacement time velocity start velocity acceleration s t v = 4 u = 4 a = 0 What is the displacement each second? How far is travelled in 3 seconds? How far is travelled in 8 seconds? time in seconds Key idea: The area under the velocity-time graph is the displacement.

Sheet 1 1] What is the velocity after 6 seconds? Velocity in m/s 1] What is the velocity after 6 seconds? 2] When is the velocity 5m/s ? 3] What is the velocity after 5 seconds? 4] What will the velocity be after 12secs? 5] What is the gradient of the line? What does this mean? 6] What is the area under the graph between 0 and 4 seconds? What does this tell us? 7] What is u (the initial velocity)? 7 m/s 2 seconds 6.5 m/s 10 m/s 0.5 20 m 4 m/s time in seconds

Sheet 1 Velocity in m/s 1] What is the velocity after 6 seconds? 2] When is the velocity 5m/s ? 3] What is the velocity after 5 seconds? 4] What will the velocity be after 12secs? 5] What is the gradient of the line? What does this mean? 6] What is the area under the graph between 0 and 4 seconds? What does this tell us? 7] What is u (the initial velocity)? 7 m/s 2 seconds 6.5 m/s 10 m/s 0.5 20 m 4 m/s time in seconds Key idea: The gradient of the velocity-time graph is the acceleration.

Sheet 2 Key idea: v = u + at m is the gradient, which is a The general form of a straight line graph is y = mx + c v m is the gradient, which is a c is the y-intercept, which is u u v = at + u t Key idea: v = u + at Here y is v and x is t. What are m and c ? What is the equation of this line?

Using the labels given and the formula for a trapezium, what is the area under the graph? Half the sum of the parallel sides, times the distance between them. Area = ½ (u+v)t Key idea: s = ½(u+v)t

Key idea: s = ut + ½at2 Key idea: s = vt – ½at2 Using the labels given and the formula for a trapezium, what is the area under the graph? v u t The height of the triangle is at (why?). The area of the triangle is ½ t × at Area = ut + ½at2 If we subtract a triangle from a larger rectangle we get Area = vt – ½at2 Key idea: s = ut + ½at2 Key idea: s = vt – ½at2

Equations of Motion v = u + at s = ½(u+v)t s = ut + ½at2 s = vt – ½at2

Equations of Motion v = u + at We want to work out s a = 9.8 u = 0 We don’t know v We need t s = ½(u+v)t s = ut + ½at2 s = vt – ½at2