Quick question about a train/car problem

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In summary, the conversation discusses a problem about a car and a truck traveling at different speeds and the time it takes for the car to reach the truck. The conversation also touches on the use of equations and variables in physics, and suggests that understanding basic calculus can be helpful in solving more complex problems.
  • #1
imagiro1
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I got a few problems like this one. The only thing I can't figure out is where to put the km. Here's what I got. A car traveling 95km/hr is 100m behind a truck traveling 75km/h. How long will it take the car to reach the truck. My 2 formulas are:

X=Xo+Vo+(1/2)at2
Car: X=95t2
Truck: X=75t2

Put both formulas equal to each other and solve for t. But where do I plug in the 100m that the car is behind? Thanks.
 
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  • #2
Welcome to PF!

Hi imagiro1! Welcome to PF! :smile:
imagiro1 said:
X=Xo+Vo+(1/2)at2
Car: X=95t2
Truck: X=75t2

Nooo :cry: …

i] it's X=Xo+Vot+(1/2)at2

ii] a (the acceleration) is obviously zero, isn't it?
Put both formulas equal to each other and solve for t. But where do I plug in the 100m that the car is behind? Thanks.

iii] that would be the Xo (a different one for each vehicle, of course) :wink:
 
  • #3
I forgot that t, I swear I got it on paper.

I ended up with Xc=.110+95t and Xt=75t, which gave me the right answer, but negative. I tried it again with Xc=95t and Xt=.110-75t and it gave me the 20 sec which is the answer.

If I change it to -.110 would that be the same thing as saying the car is .110km behind the truck?
 
  • #4
imagiro1 said:
I ended up with Xc=.110+95t and Xt=75t, which gave me the right answer, but negative. …

The car is 100m behind the truck …

so if the truck is at position 0 at time 0 (consistent with Xt = 75t), then the car is at position -100 at time 0, so Xc = … ? :smile:
 
  • #5
-.110+95t. Awesome. Thanks for the help. I'm sure I'll be back later.
 
  • #6
Imagiro, all tiny tim said is perfect but for further progresses I may suggest to try to see deeper into the methematics behind physics. I mean x=x0+v0t+1/2at^2 is not just a recipt where you input some data and it gives you another, certainly it can do so, but it is just its most superficial use. Cinematics, at the level that you are working (about the one the problem is), can be fully understood by learning and catching the basic calculus (functions, derivatives and integrals, in general).

Then, once you regard space and time as variables in a "calculus" way, you'll have no problem in solving problems like this and a lot more complicated that you never expected, even trying, before.

That's my advice, HOPE it's usefull.

Good night and good science :biggrin:
 

1. How does the velocity of the train affect the car's acceleration?

The velocity of the train does not directly affect the car's acceleration. The car's acceleration is determined by its own engine power and the friction between the wheels and the ground. However, the train's velocity can indirectly affect the car's acceleration if it is accelerating or decelerating at a rate that causes the car to speed up or slow down due to changes in air resistance or drag.

2. Can a car catch up to a train traveling at a constant speed?

Yes, it is possible for a car to catch up to a train traveling at a constant speed. If the car has a higher acceleration rate than the train and enough time, it can eventually catch up to the train.

3. How does the length of the train impact the distance needed for the car to come to a complete stop?

The length of the train does not directly impact the distance needed for the car to come to a complete stop. The distance needed for the car to stop is primarily determined by its own speed and braking power. However, a longer train may require the car to brake for a longer period of time to avoid a collision.

4. How does the weight of the train affect the car's ability to push it?

The weight of the train can significantly impact the car's ability to push it. A heavier train will require more engine power and force from the car to move it. Additionally, the friction between the train's wheels and the ground may increase with a heavier weight, making it more difficult for the car to push the train.

5. Can a car push a train uphill?

It is possible for a car to push a train uphill, but it would require a significant amount of engine power and force. The car would need to have a much higher acceleration rate than the train in order to overcome the force of gravity pulling the train downhill.

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