How to calculate the time when 2 cars are at the same position in a velocity time graph?

2016-04-17 2:17 am
Eg from 0s to 40s, car A speed increases uniformly from 0m/s to 20m/s.
From 40s onwards, car a travels at constant speed.
From 0s to 20s, car b speed increases uniformly from 0m/s to 20m/s .
From 20s onwards, car b travels at constant speed.

回答 (2)

2016-04-17 3:32 am
✔ 最佳答案
The area under a velocity vs time graph is equal to the distance the cars move.

Let’s determine the acceleration of each car. Then use the following equation to determine the distance the car moves while accelerating.
d = vi * t + ½ * a * t^2, vi = 0, t = 40
d = ½ * a * t^2
a = 20/40 = 0.5 m/s^2
d = ½ * a * t^2 = 0.25 * t^2 = 0.25 * 40^2 = 400 meters

From 0s to 20s, car b speed increases uniformly from 0m/s to 20m/s .
From 20s onwards, car b travels at constant speed.

a = 20/20 = 1 m/s^2
d = ½ * a * t^2 = 0.5 * 20^2 = 200 meters
Since both cars have the same maximum velocity the distance between the cars will always be 200 meters.
2016-04-17 3:24 am
car A never never catch up car B


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