Very elementaria kinematics question

[maria_conchita]

Homework Statement

A car starting from rest travels one quarter of a mile in 24.1 sec.
a) What is the constant acceleration?
b) What is the final speed?


2. The attempt at a solution

The solution is actually given in the book, but before posting that, I want to know why my attempt doesn't give me the same answer.

Here is what I tried:

vf = xf/t
vf = (1/4)/24.1 = 0.01037 mi/s

then:
a=vf/t
a=(0.01037 mi/s)/ 24.1s = 0.000430 mi/s^2

The way the author found the unkown was using other kinematic equations:

1) x = Vot + (1/2)(a)(t^2) where Vot = 0. To find the acceleration

2)Then with that they find "Vf" by Vf= Vo + at

I've just started to learn physics by myself and I knew it was going to be hard but I wasn't expecting getting stuck in simple problems like this one so please be patient and help me out. Maybe it's just some logic I'm not getting.

Thank you!
Eva

 

[turdferguson]

The equation v = x/t only works with constant velocity. For non constant velocity but constant acceleration, you can use the equation x=v0t + 1/2at^2. The 4 kinematic equations for constant acceleration can be easily derived using calculus.

x=v0t + 1/2at^2
v-v0 = 2ax
a = (v-v0)/t
v = (x-x0)/t

The last 2 are for average values of acceleration and velocity