Incorrect Textbook Answer involving kinematics?

In summary: So there's really no need to convert meters to kilometers (unless you want to be really precise).An even simpler sanity check is realizing that 80 m is about the length of a football field whereas 80000 km is about twice the circumference of the Earth. So there's really no need to convert meters to kilometers (unless you want to be really precise).
  • #1
canaanbowman
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1
Homework Statement
This is actually from a Calculus textbook.

A car is traveling at 100 km/hr when the driver sees an accident 80 m ahead and slams on the breaks. What constant deceleration is needed to stop the car in time to avoid a multi-car pileup.

Book says the answer is 62,500 km/hr^2.

I teach Calculus (not for very long) and the book wants students to do this from an antiderivative perspective. I did not get the answer the book states. I used my prior Physics knowledge and used the "timeless" equation for distance to check my answer and did not get that answer the the book says. I just need someone to double check my work to see if it is safe to say the book is incorrect.
Relevant Equations
vf^2 = vi^2 + 2ax
vf=0 km/hr
vi = 100 km/hr
x = 80,000 km

vf2 = vi2+2ax

0 = 100^2 + 2a(80,000)

160,000a = -10000

a = -0.0625 km/hr^2

This is off by 1,000,000 times from the textbook answer. Am I missing something with units or something or is the book wrong?
 
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  • #2
canaanbowman said:
x = 80,000 km
Which is 1,000,000 times the given 80 m
 
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  • #3
Apart from what @haruspex said above, a sanity check is always in order. If acceleration was 0.0625 km/h^2 then it would take 100 km/h / 0.0625 km/h^2 = 1600 h > 2 months to stop. This is obviously longer than necessary to cover a distance of 80 m at a mean speed of 50 km/h.
 
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  • #4
haruspex said:
Which is 1,000,000 times the given 80 m
 
  • #5
There it is! Glad to see I'm not crazy, just careless with the direction a decimal should move sometimes :)
 
  • #6
Orodruin said:
Apart from what @haruspex said above, a sanity check is always in order. If acceleration was 0.0625 km/h^2 then it would take 100 km/h / 0.0625 km/h^2 = 1600 h > 2 months to stop. This is obviously longer than necessary to cover a distance of 80 m at a mean speed of 50 km/h.
HAHA yes you are correct. Thanks! The direction a decimal moves when converting something as simple as meters to km can make or break you!
 
  • #7
canaanbowman said:
HAHA yes you are correct. Thanks! The direction a decimal moves when converting something as simple as meters to km can make or break you!
Especially if you're driving the car.
 
  • #8
kuruman said:
Especially if you're driving the car.
If I was driving the car I would probably just slam the breaks instead of starting to compute the required acceleration ;)
 
  • #9
canaanbowman said:
HAHA yes you are correct. Thanks! The direction a decimal moves when converting something as simple as meters to km can make or break you!
An even simpler sanity check is realizing that 80 m is about the length of a football field whereas 80000 km is about twice the circumference of the Earth.
 

FAQ: Incorrect Textbook Answer involving kinematics?

1) What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It involves analyzing the position, velocity, and acceleration of an object over time.

2) What is an incorrect textbook answer involving kinematics?

An incorrect textbook answer involving kinematics could be a formula or calculation that does not accurately represent the motion of an object, or a misunderstanding of the concepts and principles of kinematics.

3) How can an incorrect textbook answer involving kinematics impact my understanding of the subject?

An incorrect textbook answer can lead to misunderstandings and confusion about the principles of kinematics. It can also result in incorrect calculations and predictions of motion, which can affect the accuracy of experimental results and real-world applications.

4) What are some common misconceptions about kinematics?

Some common misconceptions about kinematics include the belief that acceleration and velocity are always directly proportional, or that an object's speed and velocity are the same thing. Another misconception is that acceleration always increases the speed of an object.

5) How can I ensure that I have the correct understanding of kinematics?

To ensure a correct understanding of kinematics, it is important to practice solving problems and applying the principles to real-world scenarios. It can also be helpful to seek guidance from a teacher or tutor, and to use reliable resources for studying, such as textbooks and online tutorials.

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