Force-Time Graphs

A force-time graph will have force (N) on the vertical axis and time (s) on the horizontal. The area under a force-time graph is Ft, which is the impulse the object will experience during that time interval (I=Ft). Recall that impulse is equal to the change in momentum of an object.

Example 1:

The force acting on an object over a 15 second interval is shown below:

 

a) Determine the force acting on the object at t=5 seconds:

At t=5 seconds, F=4N

b) When was a constant force acting on the object:

Between t=0-3s and t=7-12s

c) Calculate the total impulse acting on the object over the 15 second interval:

The total impulse acting on the object = the area under the graph. It is convenient to divide the graph into several rectangles and triangles and then calculate the sum of these areas:

Area A = 2\times 7=14

Area B = \cfrac { 1 }{ 2 } \times 4\times 4=8

Area C = 5\times 6=30

Area D = \cfrac { 1 }{ 2 } \times 3\times 6=9

Total area = 14+8+30+9= 61

Therefore, Impulse, I=61Ns