Dynamics and Space Learning Intention You will be able to: Interpret a velocity-time graph to describe the motion of an object. Calculate distance travelled from a speed-time graph. Calculate displacement from a velocity-time graph.

Velocity Time Graphs Complete the passage next to each graph Stick the graphs into your jotter. constant speed This graph shows an object travelling at a constant speed of ______.

constant acceleration This graph shows an object travelling at a constant acceleration of 2 m/s2. Its speed increases by ______ m/s every second.

Velocity time graphs are useful to physicists because they can be used to: describe the motion of the object calculate the acceleration of the object calculate the distance travelled by the object You will investigate each of these areas in turn. constant deceleration This graph shows an object travelling at a constant deceleration of 2 m/s2. Its speed decreases by ______ m/s every second.

Collect ‘speed time graphs II’ sheet Describe fully the motion of the object that produced the graph above. The first part is done for you. OA: Constant acceleration from 0 to 10 m/s in 5 seconds. A B C D O

Now- Calculate the distance travelled by the object. II III IV To calculate the distance the area under the graph must be used. Area I : Triangle area = ½ x b x h = ½ x 5 x 10 = 25m Area II : Rectangle area = l x b = 4 x 10 = 40m Area III : Triangle area = ½ x b x h = ½ x 2 x 8 = 8m Area IV : Triangle area = ½ x b x h = ½ x 3 x 18 = 27m Total Area = 100m Distance travelled = 100m

Comparing speed-time and velocity-time graphs for motion in a straight line Example A car initially travelling at 20 ms-1 in straight line to the right, and breaks and accelerates uniformly (constantly) at 5 ms-2, coming to rest in 4 s. Immediately it reverses and accelerates uniformly (constantly) at 5ms-2 in a straight line to the left for 4 s, back to where it started. The next slide shows the comparison between both types of graphs.

Velocity is a vector quantity Velocity is a vector quantity. So account is taken for the direction of travel. This is shown by the line crossing the time axis at 4 s. The straight line indicates uniform deceleration. The total mathematical area under the graph gives the total displacement. Speed is a scalar quantity. No account is taken for the direction of travel. The straight lines indicate uniform deceleration and uniform acceleration. The total area under the graph gives the total distance travelled.

Calculate the distance travelled and the displacement for the car.

Velocity time graph for a bouncing ball. On each section of the graph, writer a description of the ball’s motion. Why is area A equal to area B? Why is area A is larger then area C?

Calculate the values of the acceleration for all sections of the graph Calculate the values of the acceleration for all sections of the graph. The first part is done for you. OA: acceleration = Δv/t a = (v-u)/t a = (10 – 0)/5 a = 2m/s2. A B C D O

What can you say about the ball’s acceleration? Now justify your answer using calculations.

1 Calculate the accelerations shown in these graphs:  

2 The graph shows how the speed of a car changes. Calculate the acceleration.  

3 The graph below shows how the velocity of a car varies over a 40 s period. a) Describe the motion of the car during this 40 s period. b) Calculate the acceleration of the vehicle. c) How far does the car travel while accelerating? d) What is the total distance travelled by the car?

4 The speed of a girl on a bike was measured at 2 second intervals as she cycled across a playground. The readings are shown on the graph.   Describe the motion of the girl on the bike as she crossed the playground. Calculate the acceleration during the first six seconds. Calculate the deceleration during the last two seconds.

5 Use the graph below to answer the following questions. a) During which time is the vehicle travelling at a constant velocity? b) Calculate the values of i) the initial acceleration ii) the final deceleration c) What is the braking distance of the car? d) What is the total distance travelled? e) What is the average velocity of the car?

6 The graph below describes the motion of a cyclist for 75 seconds. a) What is the value of the maximum positive acceleration? b) Show by calculation whether the cyclist travels farther while accelerating, or while cycling at the maximum velocity.

7 An intercity train increases its speed from 0 to 60 m/s in 600 seconds. Draw a graph of the train’s motion and calculate its acceleration.  

8 The space shuttle takes 50 seconds to reach a speed of 1000 m/s from launch. Draw a graph of the shuttle’s motion and calculate its acceleration.  

9 Draw a velocity-time graph to describe the following motion:- A car accelerates from rest at 2 m/s for 8 s, then travels at a constant velocity for 12 s, finally slowing steadily to a halt in 4 s.

10 For the vehicle in the previous question, what are the values of a) the maximum velocity b) the distance travelled c) the average velocity?

11 Draw the speed-time graph for the following motion. Accelerate at 4 m/s2 for 5 seconds. Steady speed for a further 6 seconds. Accelerate at 2 m/s2 for 5 seconds Steady speed for a further 10 seconds. Decelerate at 7.5 m/s2 for 4 seconds

2000 Q21. The graph below represents the motion of a cyclist travelling between two sets of traffic lights. (a) Describe the motion of the cyclist (i) between B and C (ii) between C and D. (b) Calculate the acceleration between A and B. (c) Calculate the distance between the two sets of traffic lights. (d) Later in the journey the cyclist freewheels down a hill at constant speed. Explain this motion in terms of the forces acting on the cyclist.

A cyclist rides along a road. 2007 I2 Q22. A cyclist rides along a road. (a) Describe a method by which the average speed of the cyclist could be measured. Your description must include the following • Measurements made • Equipment used • Any necessary calculations. (b) The cyclist approaches traffic lights at a speed of 8 m/s. He sees the traffic lights turn red and 3 s later he applies the brakes. He comes to rest in a further 2.5 s. (i) Calculate the acceleration of the cyclist whilst braking. (ii) Sketch a speed time graph showing the motion of the cyclist from the moment the lights turn red until he stops at the traffic lights. Numerical values must be included. (iii) Calculate the total distance the cyclist travels from the moment the lights turn red until he stops at the traffic lights.