# Incorrect Textbook Answer involving kinematics?

• canaanbowman
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).

#### canaanbowman

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?

Last edited:
PeroK
canaanbowman said:
x = 80,000 km
Which is 1,000,000 times the given 80 m

topsquark, PeroK, Lnewqban and 1 other person
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.

topsquark and PeroK
haruspex said:
Which is 1,000,000 times the given 80 m

There it is! Glad to see I'm not crazy, just careless with the direction a decimal should move sometimes :)

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!

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.

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 ;)

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.