Calculating Power Output of Tension T on Mass M at Incline θ

[EV33]

Homework Statement

A box of mass M= 1 kg rests at the bottom ofa frictionless plane inclined at an angel theta= 20 degrees. The box is attached to a string that pulls with a constant tension T=5 N.

What is he power in Watts being delivered by the tension T as the block reaches x=50 cm

Homework Equations

P= dW/dt
w=Fd
F=ma

The Attempt at a Solution

w= (5N)(.5m)=2.5 J

Then to find the change in time I used kinematics, and to get acceleration I used Newton's second law.

Net force= T-mgsin(theta)= 5N-(1kg)(9.81 m/s^2)sin(20)=1.644782394 N

F/m=a

m=1

a=1.644782394
v=at
r=.5at^2

then I set the position equation equal to .5m to get t

.5=.5at^2

sqrt(1/a)=t =.7797327501 seconds

the from here I just put W/t

W/t=3.206226748=P

The correct answer is 6.41

Could someone please help me get going in the right direction.

Thank you.

 

[CompuChip]

Note that the distance traveled by the box, is not 0.5 m.
The box is pulled along the inclined plane, so a horizontal distance of 0.5 m corresponds to a greater distance along the plane.