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suvats question

I'm struggling with this question from Isaac physics (https://isaacphysics.org/questions/collision_conditionsii - part B).

A car and a lorry are travelling at 18ms^-1 and 10ms^-1 respectively. They are 30m apart. They simultaneously brake at 3ms^-2 and 2ms^-2 respectively (at time t = 0). After how long will they collide?

I applied s=ut+12at2s = ut + \frac{1}{2}at^2 to both vehicles:

s+30=18t+12∗3∗t2s + 30 = 18t + \frac{1}{2}*3*t^2
s=10t−12∗2∗t2s = 10t - \frac{1}{2}*2*t^2

(for them to collide, the car's displacement is 30m plus the distance that the lorry travels before they collide, hence the s + 30)

I then subtracted 30 from the first equation, and set both equations equal to each other and solved for t. However, as it is was a quadratic I got two solutions: 6 and 10. How do I know which one is correct?
(edited 6 years ago)
you get two answers because they collide twice... 6 is the right answer since that is the first time they collided.. they then collide again in the next 4 seconds which is t=10
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Original post by EA7_
you get two answers because they collide twice... 6 is the right answer since that is the first time they collided.. they then collide again in the next 4 seconds which is t=10


I don't understand how you can tell from suvats that they collide twice though. I would've thought that their new velocities after the collision would be something which can only be determined by using calculations with momentum/mass of the vehicles? And you have to know how fast they're going after the 1st collision to know how when the 2nd collision will occur.
Like if the car was really lightweight compared to the lorry then wouldn't it just rebound in the other direction?
Original post by Sint
I don't understand how you can tell from suvats that they collide twice though. I would've thought that their new velocities after the collision would be something which can only be determined by using calculations with momentum/mass of the vehicles? And you have to know how fast they're going after the 1st collision to know how when the 2nd collision will occur.
Like if the car was really lightweight compared to the lorry then wouldn't it just rebound in the other direction?


yeah, you're right but considering the information given to you in the question i.e.no mass etc were given so you can assume they meet twice if their velocities have the same magnitude and direction as before
(edited 6 years ago)
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Original post by EA7_
yeah, you're right but considering the information given to you in the question i.e.no mass etc were given so you can assume they meet twice if their velocities have the same magnitude and direction as before


Ok that makes sense. Thanks!
Original post by Sint
Ok that makes sense. Thanks!


you're welcome.. if you think about it logically, they'll never collide twice. Hence why the question doesn't go on asking about a second collision.

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