Ask Uncle Colin: Impulse and Speed

Dear Uncle Colin

I have a conceptual problem with impulse. Suppose you have a collision where your particle (of mass 1 kg) has an approach speed of 4m/s, changes direction, and leaves with a speed of 3m/s. That's an impulse of -7 units, and the ball slows down from 4m/s to 3m/s.

Suppose you have a different collision with a 'before' speed of 3m/s and an 'after' speed of 4m/s, again with the direction reversed. That also has an impulse of -7 units, but the ball has sped up.

Does impulse tell us anything about whether we've sped up or slowed down?

- Bewildering Impulses Get Me Overwhelmed

Hi, BIGMO, and thanks for your question!

In answer to your final question: no, no it doesn't. Impulse can be simply manipulated to give you the change in velocity, but not so simply the change in speed.

This is as it should be: if you only know something's speed $|v|$, and you're given its change in velocity $\delta \bf{v}$, you can't tell its new velocity unless you know its original direction (in which case you'd know its velocity). If you're working in more than one dimension, all you can say is that the new speed is between $|v| - |\delta \bf{v}|$ and $|v| + |\delta \bf{v}|$, which isn't all that helpful.

If you know about the energy transfer in a collision, you can deduce a change in speed - but impulse doesn't directly tell you anything at all about a change in speed.

Hope that helps!

- Uncle Colin


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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