A –Level Physics: Motion Graphs

Objectives: Additional skills gained: Graph evaluations Graph drawing Spec point: 10. be able to draw and interpret displacement/time, velocity/time and acceleration/time graphs Spec point: 11 know the physical quantities derived from the slopes and areas of displacement/time, velocity/time and acceleration/time graphs, including cases of non-uniform acceleration and understand how to use the quantities. Additional skills gained: Graph evaluations Graph drawing

Displacement-Time Graphs

Displacement-Time Graphs Consider a car driving at a constant 10ms-1.... Displacement (m) 40 30 20 10 The gradient of the line would be the speed! But why? 0 1 2 3 4 5 Time (s)

Distance-Time Graphs On the same graph, plot a line for a car travelling uniformly at 5ms-1 and one at 20ms-1 After that, write a brief conclusion about the relationship between the gradient/steepness of a distance-time graph line and the speed. Highlight it!

You thought you were done with me didn’t you? Not so fast… Displacement(m) 5 10 15 20 Time (s) 1 2 3 4 6 7 8 9 You thought you were done with me didn’t you? Not so fast… Displacement(m) 2 4 8 16 32 64 128 256 Time (s) 1 3 5 6 7 9 Task: Plot a separate graph for each set of data and then explain what is happening in each case with reference to the gradient of the graph

0 20 40 60 80 100 40 30 20 10 What is the speed during the first 40s? Displacement (metres) Time/s 0 20 40 60 80 100 What is the speed during the first 40s? How far is the object from the start after 100s? When was the object travelling the fastest? 0.25ms-1 40m 60-100s

Velocity-Time Graphs

Velocity-Time Graphs velocity is decreasing = negative acceleration 80 60 40 20 Velocity is increasing = accelerating Velocity (ms-1) accelerating velocity is staying the same (constant) 10 20 30 40 50 Time (s))

Velocity-Time Graphs 80 60 40 20 10 20 30 40 50 Velocity (ms-1) How can we determine the distance covered? Once you have discovered this, work out the distance covered by the car with the journey below 80 60 40 20 Velocity (ms-1) 10 20 30 40 50 Time (s))

How fast was the object going after 10 seconds? 80 60 40 20 Velocity (ms-1) Time (s) 0 10 20 30 40 50 How fast was the object going after 10 seconds? What is the acceleration from 20 to 30 seconds? What was the acceleration from 30 to 50s? How far did the object travel altogether? 40ms-1 2ms-2 -3ms-2 1700m

Fill in the description of what is happening in each journey Velocity or Speed Fill in the description of what is happening in each journey B A = B = C = D = E = A E C A= constant speed B = Uniform acceleration C = Uniform deceleration (negative acceleration) D = stationary (0m/s) E = Non-uniform acceleration (increasing acceleration) D Time

Velocity-Time Graphs When it’s curved.. In reality, objects don’t tend to have steady accelerations. To discover the acceleration at any given point (instantaneous acceleration) you work out the derivative The derivative is a tangent (straight line along a curve) that lets you work out the gradient Derivative = 5/5 = 1ms-2 Change in velocity (6-1 = 5ms-1 ) Change in Time (5 sec)

Velocity-Time Graphs When it’s curved.. If you want to know the overall or average acceleration you just need to connect the start of the graph to the end and work out the derivative (gradient) Derivative = 10/10 = 1ms-2 Change in velocity (10-0 = 10ms-1 ) Change in Time (10 sec)

Acceleration-Time Graphs Now these are new….

Acceleration-Time Graphs What quantity would you get from the area underneath the graph (integral)? = = If velocity is constant (includes being at rest), acceleration will be 0!

Gradient (derivative) Area under curve (integral) D-T, V-T, A-T Graphs Construct a summary table outlining what quantities can be calculated from the derivative and integral for each graph GRAPH Gradient (derivative) Area under curve (integral) Distance – Time Velocity – Time Acceleration - Time

D-T, V-T, A-T Graphs

Tasks and IS (sheets must be finished for IS also) Complete ‘Motion Graphs Analysis’ worksheet 1 Complete ‘Moving About’ worksheet 2 Construct a distance-time and a velocity-time graph outlining your typical journey to school each morning with sufficient estimations of speed/distance. Show an attempt to calculate instantaneous acceleration at various points in your journey and the total distance travelled. IS

Objectives: Additional skills gained: Graph evaluations Graph drawing Spec point: 10. be able to draw and interpret displacement/time, velocity/time and acceleration/time graphs Spec point: 11 know the physical quantities derived from the slopes and areas of displacement/time, velocity/time and acceleration/time graphs, including cases of non-uniform acceleration and understand how to use the quantities. Additional skills gained: Graph evaluations Graph drawing