- #1
anthonywsadler
- 2
- 1
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!
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!