Question

Work the following sample problems over interpreting graphs of motion. Assume all "points" on the graph are exactly on the intersection it lands on. Show your calculations where applicable. Make sure to include units.

Calculate the accelerations for each of the following times on the graph below.

Answer 1

The accelerations for each of the following times on the graph are:

t = 2.5 seconds: 2.4
`m/s^2`; t = 7.5 seconds: -0.8
`m/s^2`; t = 12.5 seconds: 1.6
`m/s^2`

Since the graph is of velocity, we can calculate acceleration as the difference in velocity divided by the time interval over which that change in velocity occurred.

(1) Acceleration at t = 2.5 seconds:

Acceleration = (2 - (-4)) / (2.5 - 0)

= 6 / 2.5

= 2.4
`m/s^2`

(2) Acceleration at t = 7.5 seconds:

Acceleration = (0 - 2) / (7.5 - 5)

=-2 / 2.5

= -0.8
`m/s^2`

(3) Acceleration at t = 12.5 seconds:

Acceleration = (-2 - (-6)) / (12.5 - 10)

= 4 / 2.5

= 1.6
`m/s^2`

Therefore, the accelerations for each of the following times on the graph are:

t = 2.5 seconds: 2.4
`m/s^2`

t = 7.5 seconds: -0.8
`m/s^2`

t = 12.5 seconds: 1.6
`m/s^2`