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Physics SUVAT Question

Two cars are travelling towards each other on a single-track road with equal speeds of 35m/s. When they are a distance of 500m apart, they both decide to brake.

a) What minimum equal decelerations would they require to just avoid an accident?

The brakes on one car fail and it continues with the same speed. The other car slows down and at the point of collision it has just stopped.

b) What distances have the two cars travelled when the collision occurs?
c) What time has elapsed?

Any help with working would be really appreciated!
a) If they are both travelling at the same speed, and decelerate equally, then they would meet in the middle of the 500m (travel 250m more each). Then you just use the formula : v2=u2+2as v^2 = u^2 + 2as , which can be rearranged to: a=(v2−u2)/2s a = (v^2 - u^2) / 2s .

b) Let's say that the car with the working brakes crashes after x metres, so therefore, the car without brakes crashes after travelling 500-x metres.
So therefore you can say that the following equations are both true:
For car with brakes: s=(u+v)t/2 s = (u+v)t / 2 , u=35, v=0, s=x, which gives x=35t/2 x = 35t / 2
For the car without brakes: s=(u+v)t/2 s = (u+v)t / 2 , u=35, v=35, s=500-x, which gives 500−x=35t 500-x = 35t
Just solve the two simulataneous equations.
Solving the equations will give you t, which you can use to find x.
(edited 7 years ago)
Original post by fissionchips
Two cars are travelling towards each other on a single-track road with equal speeds of 35m/s. When they are a distance of 500m apart, they both decide to brake.

a) What minimum equal decelerations would they require to just avoid an accident?

The brakes on one car fail and it continues with the same speed. The other car slows down and at the point of collision it has just stopped.

b) What distances have the two cars travelled when the collision occurs?
c) What time has elapsed?

Any help with working would be really appreciated!


Part A gives you enough data that you can just plug the values into the v^2=u^2+2as and then you can rearrange to get a.

Part B I am struggling with, would you mind checking to make sure you have put in all the data word for word cause I don't even know what calculation to use for part b.

Part C I think you take away the time it takes for impact when one car is decelerating and the other still travelling at 35ms^-1 away from the larger time where they're both decelerating at the same rate. Not 100% sure cause I haven't done any elapsed time questions before.




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Original post by BobBobson
a) If they are both travelling at the same speed, and decelerate equally, then they would meet in the middle of the 500m (travel 250m more each). Then you just use the formula : v2=u2+2as v^2 = u^2 + 2as , which can be rearranged to: a=(v2−u2)/2s a = (v^2 - u^2) / 2s .

b) Let's say that the car with the working brakes crashes after x metres, so therefore, the car without brakes crashes after travelling 500-x metres.
So therefore you can say that the following equations are both true:
For car with brakes: s=(u+v)t/2 s = (u+v)t / 2 , u=35, v=0, s=x, which gives x=35t/2 x = 35t / 2
For the car without brakes: s=(u+v)t/2 s = (u+v)t / 2 , u=35, v=35, s=500-x, which gives 500−x=35t 500-x = 35t
Just solve the two simulataneous equations.
Solving the equations will give you t, which you can use to find x.


I never thought to use simultaneous equations, I've never used them before in physics only in maths. That's a tough question.


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Original post by RossB1702
I never thought to use simultaneous equations, I've never used them before in physics only in maths. That's a tough question.


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I'm still doing my GCSEs, so I'm not 100% sure it's right but that's how I first thought to do it.
Original post by BobBobson
I'm still doing my GCSEs, so I'm not 100% sure it's right but that's how I first thought to do it.


You do AVUTS questions in GCSE's ? I did them in Scottish higher physics last year and am now doing advanced higher. Just out of curiosity what's the hardest part of GCSE physics ? I'm sure you're right btw with the simultaneous equation because it looks reasonable and I couldn't find any other method of calculations to do it, you must be pretty good at physics for knowing to do it that way.


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Original post by RossB1702
You do AVUTS questions in GCSE's ? I did them in Scottish higher physics last year and am now doing advanced higher. Just out of curiosity what's the hardest part of GCSE physics ? I'm sure you're right btw with the simultaneous equation because it looks reasonable and I couldn't find any other method of calculations to do it, you must be pretty good at physics for knowing to do it that way.


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GCSE Physics isn't hard, it's just a test of memory. The hardest stuff is stuff like nuclear fission / fusion or red shift but that's not really that hard. We learned about kinematic equations in maths, but now they removed that in the new GCSE.
Original post by BobBobson
GCSE Physics isn't hard, it's just a test of memory. The hardest stuff is stuff like nuclear fission / fusion or red shift but that's not really that hard. We learned about kinematic equations in maths, but now they removed that in the new GCSE.


Yeah, I'm sure AS or A level will challenge you a little when it comes. For now enjoy the smooth sailing. Good luck on your GCSE's!


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