Racing Problem (Kinematics)

  • Thread starter rtareen
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  • #1
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Homework Statement:

The motorcycle first takes the lead because its (constant) acceleration am = 8.40 m/s2 is greater than the car’s (constant) acceleration ac = 5.60 m/s2, but it soon loses to the car because it reaches its greatest speed vm = 58.8 m/s before the car reaches its greatest speed vc = 106 m/s. How long does the car take to reach the motorcycle?

Relevant Equations:

ac = 5.6m/s2
am = 8.40m/s2
vcmax = 106m/s
vmmax = 58.8 m/s
2E0E3B09-8DA2-4F5E-9AF3-E51F178F3ED7.jpeg


Here is my attempt at the solution but I got the wrong answer. The right answer is t=16.6s. I know from the book (this is an example problem) that the motorcycle reaches its max speed at t=7.0s. But I don’t know where I made the mistake that is causing me to get the wrong answer afterwords.
 

Answers and Replies

  • #2
gneill
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Your error lies in how you calculate the motorcycle position.
1576983971342.png

You're covering the time between 0 s and 7.0 seconds twice, since your xmo already covered that once.
 
  • #3
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Your error lies in how you calculate the motorcycle position.
View attachment 254545
You're covering the time between 0 s and 7.0 seconds twice, since your xmo already covered that once.
I don’t see why that’s a mistake. At t=7.0s the equation for the motorcycles position changes. It no longer has an acceleration, just a constant velocity. xmo is the starting point for this new position function.
 
  • #4
gneill
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xmo is the starting point for this new position function.
The way it is written means that the ##v \times t## term assumes a starting time of ##t = 0##. That is not the case if it's contribution should only "kick in" at ##t = 7 sec##.
 
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  • #5
PeroK
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I don’t see why that’s a mistake. At t=7.0s the equation for the motorcycles position changes. It no longer has an acceleration, just a constant velocity. xmo is the starting point for this new position function.
It seems that your answer of ##9.6s## is the time starting from when the motorcycle reaches its maximum speed (after ##7s##). The answer of ##16.6s## is the time from when both vehicles start. I.e. your answer plus the ##7s##.

PS after ##9.6s## the speed of the car is ##53.76 m/s##, so it's not yet reached the speed of the motorcycle.
 
Last edited:
  • #6
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It seems that your answer of ##9.6s## is the time starting from when the motorcycle reaches its maximum speed (after ##7s##). The answer of ##16.6s## is the time from when both vehicles start. I.e. your answer plus the ##7s##.

PS after ##9.6s## the speed of the car is ##53.76 m/s##, so it's not yet reached the speed of the motorcycle.
So I just need to add 7s to the answer I got and I’ll have the correct answer. I can see why now. Thanks!
 

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