Incorrect Textbook Answer involving kinematics?

[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

v_f=0 km/hr
v_i = 100 km/hr
x = 80,000 km

v_f² = v_i²+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?

 

[haruspex]

x = 80,000 km

Which is 1,000,000 times the given 80 m

 

[Orodruin]

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.

 

[canaanbowman]

Which is 1,000,000 times the given 80 m

 

[canaanbowman]

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

 

[canaanbowman]

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!

 

[kuruman]

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.

 

[Orodruin]

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 ;)

 

[vela]

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.