Solving for acceleration of a piston

[Palladian1881]

Homework Statement

The piston has a displacement of 10 cm and there are 50 cycles per second. Calculate the average acceleration that occurs between the start/stop point and the middle of the cycle. This value has to do with evenly accelerated movement. This can be described according to the formula d = .5a * t².
To solve:
-Compute the average velocity using a full cycle.
-Calculate how long the piston needs to travel 5 cm from the top of the cycle to the middle, which will give us the value for t. Then use a = 2 * d / t² to calculate the acceleration.

Homework Equations

d = .5a * t²
a = 2 * d / t²
v = d / t

The Attempt at a Solution

50 cycles per second = 1 cycle takes 20 milliseconds.
velocity = d / t
10 m/s = 20cm / 50 ms (total cycle distance is 20cm because the displacement is 10cm)
How long the piston takes to travel 5 cm: 5 ms (so t = .005s)
a = 2 * d / t²
a = 2 * .1m / .005s² = 40 m/s²
But this isn't the right answer! Please help!

 

[Andrew Mason]

Why are you using .1 m for d? d is the distance traveled in time t

AM