Question

Could you help with this question: Construct position-time and velocity-time graphs for the seat cushion. You can plot the average velocity for each second (displacement between data points / time interval of 1 s) at the midpoint of the time interval (at 0.5 s, next average speed at 1.5 s) to properly plot the velocity-time graph.

Answer 1

The given table contains values for position and corresponding time. To plot the position time graph, we would plot the position values on the y axis and the time values on the x axis. The graph is shown below

For the velocity times graph, the table would be as shown below

Between t = 0 and t = 1,

average time = (0 + 1)/2 = 0.5

average velocity = (4.5 - 0)/1 = 4.5

Between t = 1 and t = 2,

average time = (1 + 2)/2 = 1.5

average velocity = (12 - 4.5)/1 = 7.5

Between t = 2 and t = 3,

average time = (2 + 3)/2 = 2.5

average velocity = (21 - 12)/1 = 9

Between t = 3 and t = 4,

average time = (3 + 4)/2 = 3.5

average velocity = (31 - 21)/1 = 10

Between t = 4 and t = 5,

average time = (4 + 5)/2 = 4.5

average velocity = (41.5 - 31)/1 = 10.5

Between t = 5 and t = 6,

average time = (5 + 6)/2 = 5.5

average velocity = (51.5 - 41.5)/1 = 10

Between t = 6 and t = 7,

average time = (6 + 7)/2 = 6.5

average velocity= (62 - 51.5)/1 = 10.5

Between t = 7 and t = 8,

average time = (7 + 8)/2 = 7.5

average velocity = (72 - 62)/1 = 10

We would plot the change in time in the x axis and the average velocity in the y axis. The velocity time graph is shown below