Maximum distance apart from both cars before Car B catches up with Car B

In summary, the problem involves two cars, A and B, with different initial velocities and a velocity-time graph is used to find the maximum distance between them before B catches up with A. The maximum distance will occur at one of the "joins" on the graph, where the two cars are either getting further apart or closer together.
  • #1
cyy91
8
0

Homework Statement



Car A travel at uniform velocity at 20 metre per second from t=0s.
Car B starts with 5 metre per second during t=0s and accelerates uniformly to 30 metre per second in t=30s.It travels at constant velocity of 30 metre per second from there onwards

Homework Equations


The Attempt at a Solution


A velocity-time graph is plotted for this question.

But i just simply don't know wad to do regarding the maximum distance between both of the cars before Car B catches up with Car A.
I need urgent help and i mean it,thanks...
what can i do with the graph to solve this question?
 
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  • #2
Welcome to PF!

Hi cyy91! Welcome to PF! :smile:

The distance between the cars at any time is the horizontal distance between the two graphs at that value of t.

There are no curves … the graphs is only straight lines … and two straight lines either get continually further apart, or continually closer together … so the maximum distance must be at one of the "joins". :wink:
 
  • #3
thx alot...understood...
 

1. What is the maximum distance apart that both cars can be before Car B catches up with Car A?

The maximum distance apart is dependent on the initial speeds of both cars. The faster Car A is traveling, the further apart the cars can be before Car B catches up. The slower Car A is traveling, the closer the cars must be before Car B catches up.

2. What factors influence the maximum distance apart for Car B to catch up with Car A?

The main factor influencing the maximum distance apart is the speed of Car A. Other factors that may play a role include the acceleration and deceleration capabilities of both cars, as well as the terrain and any obstacles in the path of the cars.

3. Is there a specific equation or formula for calculating the maximum distance apart for Car B to catch up?

Yes, there is a formula that can be used to calculate the maximum distance apart. It takes into account the initial speeds of both cars, as well as their acceleration and deceleration rates. This formula can be found in most physics textbooks or online resources.

4. Can the maximum distance apart be greater than the initial distance between the cars?

No, the maximum distance apart cannot be greater than the initial distance between the cars. This is because as Car B catches up with Car A, the distance between them decreases. Therefore, the maximum distance apart is always equal to or less than the initial distance between the cars.

5. How can I determine the maximum distance apart for a specific scenario?

You can determine the maximum distance apart by plugging in the values for the initial speeds, acceleration and deceleration rates of both cars into the equation or formula mentioned earlier. It is important to use consistent units and to double check your calculations to ensure accuracy.

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