Relative motion with constant acceleration

• MatinSAR
In summary, the conversation discusses a kinematic problem where two cars are decelerating at the same rate but have different initial speeds. The question posed is whether or not the cars will stop at the same time. After some discussion and analysis, it is determined that the cars will not stop at the same time and one must consider what happens when one car stops. The mistake is found and it is acknowledged that this is a good problem to think about. The answer is determined to be 10 seconds.
MatinSAR
Homework Statement
Two cars A and B are moving towards each other with speeds of 8m/s and 12m/s respectively. When the distance between the two cars is 102m, both drivers brake at the same time. If both cars decelerate with an acceleration of 1 m/s², how many seconds after the moment of braking will the two cars hit each other?
Relevant Equations
X=X0+V0t+(1/2)at^2
I think the question is wrong.

But it should be wrong because :

I think the question is wrong … But I'm not sure …

The acceleration of B can’t be positive; its velocity is never increasing.

MatinSAR
Lnewqban said:
The acceleration of B can’t be positive; its velocity is never increasing.
Slowing down means the acceleration and velocity have opposite signs, which they do.
The OP is taking the same direction as positive for all accelerations and velocities.

MatinSAR and topsquark
Lnewqban said:
The acceleration of B can’t be positive; its velocity is never increasing.
haruspex said:
Slowing down means the acceleration and velocity have opposite signs, which they do.
The OP is taking the same direction as positive for all accelerations and velocities.

According to the question, the motion is decelerating.
So the sign of speed and acceleration of car A must be different. The same for B.
I observed this for both cars A and B. Could you please tell me where my mistake is ?!

MatinSAR said:
Since they are initially at different speeds but decelerating at the same rate, they will not come to a stop at the same time. So you need to think about what happens when one car stops. You can’t assume it maintains the same acceleration.

erobz, MatinSAR, topsquark and 1 other person
haruspex said:
Since they are initially at different speeds but decelerating at the same rate, they will not come to a stop at the same time. So you need to think about what happens when one car stops. You can’t assume it maintains the same acceleration.
I've founded my mistake.

MatinSAR said:
I've founded my mistake.
I like how we must stop and think\reason about this kinematic problem (not @haruspex ‘s first rodeo). I don’t think I’ve ever saw one like this. Good problem!

topsquark
erobz said:
I like how we must stop and think\reason about this kinematic problem (not @haruspex ‘s first rodeo). I don’t think I’ve ever saw one like this. Good problem!
Yes it was a good problem.
erobz said:
I think the answer is 10 seconds.

erobz
MatinSAR said:
I think the answer is 10 seconds.
I think so too. The first car stops after 8 seconds, having traveled 32 metres. The second car travels 70 metres in 10 seconds.

SolarisOne, MatinSAR and erobz

1. What is relative motion with constant acceleration?

Relative motion with constant acceleration refers to the movement of an object in relation to another object while experiencing a constant change in velocity. This type of motion is often described using equations such as the displacement equation, velocity equation, and acceleration equation.

2. How is relative motion with constant acceleration different from uniform motion?

Uniform motion refers to the movement of an object at a constant velocity, while relative motion with constant acceleration involves a changing velocity. This means that the object's speed and/or direction is constantly changing over time.

3. What is the formula for calculating displacement in relative motion with constant acceleration?

The formula for displacement in relative motion with constant acceleration is:
Δx = v0t + ½at2,
where v0 is the initial velocity, t is the time, and a is the acceleration.

4. How does acceleration affect the displacement in relative motion?

Acceleration has a direct effect on the displacement in relative motion. The greater the acceleration, the greater the change in velocity and therefore the greater the displacement over a given time period. This means that a higher acceleration will result in a larger displacement.

5. Can relative motion with constant acceleration be negative?

Yes, relative motion with constant acceleration can be negative. This means that the object is moving in the opposite direction of the positive direction that was defined. For example, if a car is driving east and then starts to slow down and move west, its acceleration would be negative.

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