Homework Help: Question about fiding speed and distance

1. Nov 11, 2013

sofiasherwood

I had a test earlier today and one question was,

A 20kg object initially at rest is accelerated at constant power of 12.0w. After 9.0s it has moved 56.0m. Find its speed at t=6.0s and its position at that instant.

I got v=6 and distance=36m are these values correct?

2. Nov 11, 2013

HallsofIvy

I started to say that this makes no sense. An object accelerates at a constant acceleration measured in $m/s^2$. That acceleration may be caused by a constant force, measured in Newtons, but not a constant power measured in watts.

But the "12.0 w" really has nothing to do with the problem and can be ignored. If an object accelerates from rest at constant acceleration, a $m/s^2$, then after time, t, it will have speed $at$ m/s and will have moved distance $(1/)at^2$ m.

They do not look at all right to me. How did you get them?

3. Nov 11, 2013

sofiasherwood

P*t=W
12*9=108
therefore W=108joules
W=F*displacement
F=108/56
F=1.93N

F=ma
a=1.93/20
a=0.1

so at t=6
Pt=W
12*6=72joules
W=72joules

W=F*displacement
displacement=72/(20*0.1)
displacement=36m

P=Fv
v=12/(20*0.1)
v=6

4. Nov 11, 2013

Staff: Mentor

Halls, it doesn't say constant acceleration. Constant power is what you might get from a car with a continuously variable transmission.

5. Nov 11, 2013

sofiasherwood

I am assuming the acceleration is constant. Is that right?

6. Nov 11, 2013

sofiasherwood

Have I gone wrong somewhere?

7. Nov 11, 2013

Enigman

8. Nov 11, 2013

sofiasherwood

This is the question given in the test word for word. The question confused me for ages, in the end I just assumed acceleration was constant. I don't know how you could work it out any other way.

9. Nov 11, 2013

Enigman

10. Nov 11, 2013

Try not to round of numbers.Use fractions.

11. Nov 11, 2013

Enigman

Acceleration can not be constant...
P=dW/dt
P=d(∫F.dx)/dt
P=F.dx/dt
P=Fv
If a is const.
P=ma*(at)
P=ma2t
Then Power is not constant as given in the question...

12. Nov 12, 2013

f95toli

I saw this question when it was in the other section, it looked fishy to me then and I just had a go at it. Unless I am missing something it does not have a solution.
The way the question is formulated you will -as Enigman pointed out- end up with a 2nd order ODE for the position; but then the constants are over-determined.

I wonder if this is a case of the teacher trying to add a red herring (constant power) without realizing that this implies that the accelaration can not be constant.