NOTES p.13 Balls in the Air!

Graphs for Objects Thrown Up Try to draw graphs of speed, velocity and acceleration against time for a ball thrown vertically upwards at 20ms-1 and taking 4 s to land. 3 4 t(s) 2 acceleration (ms-2) -10 3 20 4 t(s) Speed (ms-1) 2 3 20 -20 4 t(s) velocity (ms-1) 2 What distance does the ball travel during the 4 s? What is the displacement of the ball after 4 s? What is the speed of the ball at 4 s? What is the velocity of the ball at 4s? Area = 40 m Area = 20 - 20 = 0 m 20 m/s -20 ms-1

Distance travelled = area below a speed-time graph Displacement = Area below a velocity-time graph with areas below the time axis being negative!

Acceleration, due to gravity, is 10 ms-2 20 Speed (ms-1) t(s) 2 3 4 t(s) 2 3 4 -10 20 velocity (ms-1) Q5. The sense of the motion changes after 2 s, yet the acceleration graph is one continuous line. Explain why. t(s) 2 3 4 Answer Acceleration, due to gravity, is 10 ms-2 (rounded here for simplicity) DOWNWARDS, for the whole journey. -20

AB – ball travelling down BC – bounce (in contact) Over to you – Draw the velocity-time graph of a ball that is released, drops and bounces twice. In this case take downwards as –ve and upwards as +ve. (Numerical axes are not required and assume no energy is lost due to negligible contact time with ground) t(s) velocity (ms-1) A B C D E F AB – ball travelling down BC – bounce (in contact) CD – travelling up to maximum height DE – travelling downwards and speeding up EF – second bounce Over to you, again – 1. Complete the “Bouncing Ball” Graphs handout. 2. Q. 29 - 32 from the Mechanics and Properties of Matter problems.

Answers to Q. 27 – 32 29. velocity (ms-1) time(s) 5 10 30 5 5 10 30 5 acceleration (ms-2) -0.5 2 3 4 10 time(s) -10