Velocity – time graphs and acceleration Example A police car chasing a criminal increases from 20 m/s to 30 m/s in 5 seconds. Calculate the car’s acceleration. (m/s) a = acceleration (m/s2) t = time taken (s) a = (v-u) / t a = (30-20) / 5 a = 2 m/s2

Difference between velocity and acceleration

v - t graph – calculating acceleration B C Velocity Use the graph calculate the acceleration between a) A and B b) B and C You need to work out the change in speed and the time taken, then use the equation. A

v- t graph – calculating acceleration B C A to B Velocity increases Acceleration a = (8-0)/ 4 a= 2 m/s2 Velocity B- C Constant velocity = 8m/s a = (8-8) /6 = 0 No acceleration A

v – t graph – calculating distance travelled On a velocity time graph the distance travelled is the area under the graph C B Velocity A - B Calculate the distance travelled between A and B B - C Calculate the distance travelled between B and C A

v – t graph – calculating distance travelled On a velocity time graph the distance travelled is the area under the graph A to B Area is a triangle Area = (baseXheight) / 2 = (8 X 4) / 2 = 16 m Velocity B B- C Area is a rectangle Area =baseXheight = 8 X 6 = 48 m C A

What is the velocity between 2 and 4 s? What is the average velocity between 1 and 2 s? Find the distance travelled between 2 and 4 s.  What is the distance travelled between 2 and 5 s?    What is the average velocity between 2 and 5 s?

What is the velocity between 2 and 4 s? = 20m/s What is the average velocity between 1 and 2 s? = 10m/s Find the distance travelled between 2 and 4 s. = 40m  What is the distance travelled between 2 and 5 s? = 50m What is the average velocity between 2 and 5 s? = 16.6m/s Velocity = distance/time = 50/3 =16.6m/s

Velocity time graphs Gradient of the graph is the acceleration Steeper the graph the higher the acceleration. If the graph is horizontal it is constant speed or terminal speed To calculate distance travelled, work out area under the graph

Velocity time graphs Speed always goes on the y axis Time on the x axis Sketch speed time graphs for the following A car speeding up A car travelling at a constant 20m/s A car slowing down

Velocity time graphs We can use velocity time graphs to show a car’s acceleration. Jane pulls out in her car. Part 1 - She speeds up from rest to 20m/s over 10 seconds. Part 2 - She then drives at a constant speed of 20m/s for 20 seconds. Part 3 - Then she slows down from 20m/s to 0m/s in 5 seconds. Draw a velocity-time graph of the car journey. Calculate the acceleration of the car in each part. Calculate the distance travelled in each part. Calculate the total distance travelled.

http://www.bbc.co.uk/learningzone/clips/speed-time- graphs/10673.html

Plenary What is the difference between speed and velocity? What are the units of speed and acceleration? What is the equation for acceleration? How do you calculate acceleration from a v – t graph? How to you calculate distance travelled from a v- t graph?

Plenary What is the difference between speed and velocity? Speed is a measurement of the distance covered in a specified time. Velocity is speed in a specific direction. What are the units of speed and acceleration? Speed is measured in m/s. Acceleration is measured in m/s2 What is the equation for acceleration? a=(v-u)/t How do you calculate acceleration from a v – t graph? Calculate the gradient of the line. How to you calculate distance travelled from a v- t graph? Measure the area under the line.

Velocity time graph Bob jumps out of a plane. He speed starts at 0. He speeds up to 40m/s over 20 seconds. Then he reaches terminal (constant) speed of 20 m/s for 30 seconds. He opens his parachute and his speed drops to 5 m/s immediately. He carries on falling for 5 m/s for 30 seconds. Then he hits the ground. Sketch a graph of his speed against time Calculate his acceleration in first 10 seconds. Calculate the distance he travels in the first 10 seconds