Simple Work Problem Disagreeing with Kinematics

[anthonywsadler]

I have the following problem: "A box with a mass of 10 kg is accelerated by 10 m/s/s over a distance of 10 meters. What is the kinetic energy of the box (assuming no friction)"

Using work...

Work = K.E.
F * D = K.E.
m*a*D = K.E. = 10 kg * 10 m/s/s * 10 m = 1000 Joules

However, using kinematics...

x = vo*t + at^2
10 m = 0 m/s + 10 m/s/s * t^2
10 m/10 m/s/s = t^2
t = 1 sec (the time it takes the box to go 10 meters)

vf = vo*t + a*t
vf = a*t = 10 m/s/s * 1 s = 10 m/s

KE = 1/2*m*v^2 = 1/2*10kg*(10 m/s)^2 = 500 Joules

Where is this factor of 2 difference coming from? Is the issue coming from how the problem is written? Thank you for your help!

 

[berkeman]

Welcome to PhysicsForums.

x = vo*t + at^2

Check this?

 

[anthonywsadler]

Thanks! This is what happens when I don't get enough sleep, I leave out a factor of 1/2!

The box takes sqrt(2) seconds to reach 10 meters, which gives a final velocity of 14.14 m/s. The kinetic energy is indeed 1000 Joules.

Sorry and thank you!

 

[hutchphd]

A well-asked question is easy to answer. Welcome.

 

[hmmm27]

The dimensions used in the question are mass, acceleration and distance. Remind anybody of a certain energy formula that uses those and only those dimensions ?