What is the acceleration of the car

[colin_delecia]

Homework Statement

A car slows down from 25 to rest in a distance of 75 .
What is the acceleration of the car.

I've been fiddling with this problem pretty much all night but can't seem to get to a correct answer, help would be apprechiated.

Homework Equations

x = x0 + v0t + 1/2at^2
d = 1/2(v0 +v)t

The Attempt at a Solution

x = x0 + v0t + 1/2at^2

75m = (25m/s)(60.5s) + 1/2a(60.5s)^2

75m = 1512.5m + 1/2a(60.5s)(60.5s)
75m = 1512.5m + 1/2a(3660.25s^2)

75m - 1512.5m = 1512.4m - 1512.4m 1/2a(3660.25s^2)
-1437.5m = .5a(3660.25s^2)
------ ----------------

.5 .5


-2875 = a(3660.25s^2)
------ -------------
3660.25 3660.25s^2


-.79m/s2

AND

-25m/s
------
60.5s = -.42m/s2

 

[quietrain]

em i don't understand how you got your time? anyway

notice this question doesn't give you time.

so you use the equation of motion that doesn't involve time, which is

v² = u² + 2as

now , v² = 0 , because final car velocity = 0
u² = 25 as stated in question
s = 75

so 0 = 25 + 2a(75)
a = -25/(2x75) = -0.16

so the negative sign tells you the acceleration is opposite to the direction of the +25 m/s velocity , i.e, the car is decelerating .