Kinematics Question -- 2 Runners Racing Each Other

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SUMMARY

In the kinematics problem involving runners Dave and Andrew, Dave runs at a constant speed of 20 m/s and accelerates at 1.0 m/s² after being passed by Andrew. After 2 seconds, during which Andrew maintains a constant speed, Dave catches up to him in 25 seconds. The calculations reveal that Andrew's velocity is determined to be 30.7 m/s, factoring in the distance Andrew covers during the initial 2 seconds before Dave begins to accelerate.

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Homework Statement



Dave and Andrew are racing. Dave running at a constant speed of 20m/s is passed by Andrew. 2.0s after Andrew passes, Dave accelerates at 1.0m/s^2 until he catches up with Andrew 25s later. What is Andrew's velocity (he does not accelerate)?

Homework Equations



Kinematics Formulas.

The Attempt at a Solution


d=vit+1/2at^2
=(20)(25)+1/2(1)(25)^2
=812.5

Dave travels 812.5m.
v=d/t
=(812.5)(25+2)
=30.7m/s

I'm not sure if the way I did it was correct. Can someone please tell me how to do it. If you think I'm right though can you please tell me. Thanks!
 
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You seem to have forgotten that 2 seconds went by before Dave accelerated. during these two seconds both runners moved.
 
Usain Bolt runs at 12.4m/s but can only sustain that speed for 20 or 30m. So there is something unrealistic about the numbers you are given.

With that said, looks like you calculated "d" right but missing the distance that Andrew is ahead after the first 2 seconds.
 
Last edited:

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