Stuck on this simple physics problem.

[pokeefer]

Homework Statement

Two buses are moving at constant speeds, in the same direction, the first at 42 km/h and the second at 54 km/h. They are 18 km apart. How long will it take the second bus to catch up to the first? (4 marks)

Homework Equations

average velocity = d/t

The Attempt at a Solution

Ok well first I tried to make a table of the graph but then I remembered that they were 18 km apart so then I had to rethink and I'm still really stuck on this.

 

[rl.bhat]

When they catch up, the first bus moves through x km and second bus moves through x + 18 km, and they must have taken the same time to cover that distance.

Can you proceed now?

 

[pokeefer]

What would be a formula that could solve for this?

Or do I have to use a table?

 

[rl.bhat]

Velocity = x/t. So t = x/v.

Since t is the same

x/v1 = (x+18)/v2

v1 and v2 are given. Solve for x.

 

[rwisz]

I understand that the key to solving any problem is to first clearly define the variables and equations involved. In this case, we have two buses moving at constant speeds, so we can use the equation for average velocity, which is distance divided by time. We also know that the buses are 18 km apart and that the second bus is trying to catch up to the first.

To solve this problem, we need to consider the relative motion between the two buses. Since they are moving in the same direction, the second bus is trying to close the distance between them. This means that the relative velocity between the two buses is the difference between their speeds, which in this case is 54 km/h - 42 km/h = 12 km/h.

Now, we can use the equation for average velocity to determine the time it will take for the second bus to catch up to the first. We know that the distance between the two buses is 18 km, and the relative velocity between them is 12 km/h. Therefore, we can set up the following equation:

18 km = (12 km/h) x t

Solving for t, we get t = 18 km / 12 km/h = 1.5 hours.

So, it will take the second bus 1.5 hours to catch up to the first bus. I hope this explanation helps you understand the problem better. Remember, when solving physics problems, it is important to clearly define the variables and equations involved and to consider the relative motion between the objects. Keep practicing and you will become more confident in solving these types of problems.