# Using free fall acceleration to find another acceleration

## Homework Statement

A test of the prototype of a new automobile
shows that the minimum distance for a con-
trolled stop from 100 km/h to zero is 41 m.
Find the acceleration, assuming it to be
constant as a fraction of the free-fall accel-
eration. The acceleration due to gravity is
9.81 m/s2.

## Homework Equations

Kinematics equations

## The Attempt at a Solution

I'm actually unsure how to even begin this problem. The statement has me confused, such as what they mean by "a fraction of the free-fall acceleration."

ideasrule
Homework Helper
It means 9.8 m/s^2 would be 1g, 19.6 m/s^2 would be 2g, etc.

Do you know any kinematic equation that relates final speed, initial speed, acceleration, and distance?

v^2 = Vo^2 + 2ax -> a = v^2 - vo^2 / 2x -> 0 - (27.778 m/s^2) / 2(41m) = -9.4098

From here I did this equation as a fraction of the free fall acceleration:

-9.4098 m/s^2 / -9.80m/s^2 -> A = .9602g.

Whatever I might have done, I got the question wrong. Can you maybe help me elaborate on my errors?

gneill
Mentor
Your methodology is okay. The resulting acceleration value, whether or not in units of g, should still be negative. You might also want to pay attention to the number of significant figures that are warranted.