# Find deceleration, given initial velocity and final distance

1. Jun 10, 2013

### EricPowell

1. The problem statement, all variables and given/known data
A car travelling at 88ft/s skids 176ft after its brakes are applied. The deceleration provided by the braking system is constant. What is its value?

3. The attempt at a solution
$$v_0=88 \\ v_f=0 \\ d_0=0 \\ d_f=176$$
$$d(t)=\int88\,dt \\ d(t)=88t+c \\ 0=88(0)+C \\ C=0 \\ 176=88t \\ t=2s$$
$$a=\frac{Δv}{Δt} \\ =\frac{-88}{2} \\ =-44ft/s$$
The answer key of the textbook says that the deceleration is -22ft/s2. :(

2. Jun 10, 2013

### milesyoung

You have assumed motion with constant velocity in finding d(t). You need to use the kinematic relationships that deal with motion with constant acceleration:
http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html

Those should give you 2 equations in 2 unknowns.