Graphs of Motion
For Today (b) carry out average speed and acceleration calculations. (c) apply graphical methods to represent displacement, speed, velocity and acceleration; (d) determine velocity from the gradient of a displacement against time graph; (e) determine displacement from the area under a velocity against time graph;
A reminder Average speed = distance travelled time taken d t S x
Distance against time graphs
Distance/time graph Distance /m 2 4 6 8 10 12 14 16 18 20 Time (run 1)/s 3.39 5.25 7.32 10.08 11.99 14.63 16.62 19.29 20.87 23.12 Time (run 2)/s 1.38 2.27 3.42 4.53 5.54 7.01 7.87 9.35 10.31 9.75 Time (run 3)/s 3.07 4.79 6.00 6.93 7.69 8.14 8.81 9.32 9.73 9.62
No movement? distance time
No movement distance time
Constant speed? distance time
Constant speed distance time
Constant speed distance The gradient of this graph gives the speed time
How would the graph look different for a faster constant speed? distance time
Constant speed fast distance time
How would the graph look different for a slower constant speed? fast How would the graph look different for a slower constant speed? distance time
Constant speed fast distance slow time
Getting faster? (accelerating) distance time
Getting faster (accelerating) distance time
Examples distance time
A car accelerating from rest and then hitting a wall distance time
A car accelerating from stop and then hitting a wall distance time
Speed against time graphs
No movement? speed time
No movement speed time
Constant speed? speed time
Constant speed speed time
How would the graph look different for a faster constant speed? time
Constant speed speed fast time
How would the graph look different for a slower constant speed? fast time
Constant speed speed fast slow time
Getting faster? (accelerating) speed time
Getting faster? (accelerating) speed Constant acceleration time
Getting faster? (accelerating) speed The gradient of this graph gives the acceleration time
Getting faster? (accelerating) v The gradient of this graph gives the acceleration speed a = v – u t (v= final speed, u = initial speed) u time
Getting faster? (accelerating) speed The area under the graph gives the distance travelled time
Example: speed time
A dog falling from a tall building (no air resistance) speed time
A dog falling from a tall building (no air resistance) speed time
A dog falling from a tall building (no air resistance) speed Area = height of building time
Be careful! speed time distance time
No movement speed time distance time
Constant speed speed time distance time Area = distance travelled
Constant acceleration speed time Gradient = acceleration a = (v-u)/t distance time Area = distance travelled