Motion and Position-Time Graphs

[Jacobpm64]

A police officer clocked a driver going 20 mph over the speed limit just as the driver passed a slower car. He arrested both drivers. The judge agreed that both were guilty, saying, "If the two cars were next to each other, they must have been going the same speed." Are the judge and police officer correct? Explain with a sketch, a motion diagram, and a position-time graph.

Uhmm.. I'm not sure at all how to think about this.. If i look at it one way.. it looks like it would have to be the same.. because they'd meet at the same point where the distance / time would be the same on the graph.. but if i think about it.. it wouldn't be very smart to say that they'd have to be moving at the same speed.. or would it? I'm confused

 

[siddharth]

Think about this. One car, initially at the origin (say x=0) is going with a constant velocity of 100 m/s. Another car, initially 100m away(x=100) is going with a constant velocity of 50 m/s in the same direction. Will the cars pass? If so,what will the velocities of the cars be?

 

[quicknote]

I cannot comment on the legality or fairness of the judge's decision. However, from a scientific perspective, the judge's statement is not entirely accurate.

Firstly, the fact that both cars were next to each other at one point does not necessarily mean they were traveling at the same speed. It is possible that one car was initially traveling faster than the other and then slowed down, while the other car maintained a constant speed. Therefore, it is not safe to assume that both cars were going the same speed based on their relative positions.

To better understand this situation, we can look at it from a motion diagram and a position-time graph. A motion diagram shows the position of an object at different points in time, while a position-time graph plots the position of an object over time.

In this scenario, let's assume that the slower car was traveling at a constant speed of 40 mph and the faster car was initially traveling at 60 mph and then slowed down to 40 mph as it passed the slower car. The motion diagram would show the slower car maintaining a constant position while the faster car moves ahead and then slows down to match the slower car's position (see diagram below).

Motion Diagram:

Slower car: ___________|_________|_________|_________|_________

Faster car: ___________|_________|_________|_________|_________|_________

Time: _________0________|_________1________|_________2________|_________3________|_________4________|

Position-Time Graph:

Position (miles) ___________|_________|_________|_________|_________|_________|_________|_________|_________

Time (hours) _________0________|_________1________|_________2________|_________3________|_________4________|

From this diagram and graph, we can see that while the two cars were next to each other at time 2, they were not traveling at the same speed. The faster car had to slow down to match the slower car's position.

In conclusion, the judge's statement that the cars must have been going the same speed because they were next to each other is not accurate. The position-time graph and motion diagram show that the cars were not traveling at the same speed, even though they were next to each other at one point. It is important to look at both the position and time data to fully understand the motion of objects.