# Homework Help: A force that changes in time

1. Feb 20, 2015

### goonking

http://imgur.com/DZPb7oa

How do I even start that? I replace t with 7.6

so F(7.6) = 13.78 which is the force, correct?

F= ma

13.78 = 6 kg x a

a = 2.3 m/s2

is this correct so far? am i on the right route?

2. Feb 20, 2015

### PeroK

You need to use the Homework Template.

Have you learned the integral calculus?

3. Feb 20, 2015

### goonking

very briefly. is it required to do this problem?

isn't integral calculus just +1 to the exponent and divide the whole term by the new exponent??

hint says the integral of acceleration is velocity but the only equation they give us is for force.

4. Feb 20, 2015

### Staff: Mentor

The force is not constant, it is continually changing with time.

Using calculus, what is the general expression for velocity in terms of acceleration?

5. Feb 20, 2015

### goonking

integral i believe? since derivative of velocity gives you acceleration.

6. Feb 20, 2015

### Staff: Mentor

If you click on the capital sigma $(\Sigma)$ in the toolbar of the text entry box below you will see some useful symbols appear; among them is an integral sign.

7. Feb 20, 2015

### goonking

so do I find the integral of F(t) to give me velocity?

8. Feb 20, 2015

### Staff: Mentor

That's close, but you have to be exact if you hope to get the right answer.

I hoped that by my pointing out the integral sign, you might be encouraged to use it.

9. Feb 20, 2015

### goonking

F(t) is the only equation there I can integrate, how can I get a more exact answer?

10. Feb 20, 2015

### Staff: Mentor

You know that the time integral of force doesn't have units of metres/second. So how can you convert your force into something that can be integrated to give velocity?

11. Feb 22, 2015

### goonking

convert force to acceleration? F = ma?

12. Feb 22, 2015

### Staff: Mentor

Right. And you can see that the "conversion" involves a proportionality constant.

13. Feb 22, 2015

### goonking

I'm getting the answer to be 17.45 meters/sec.

is that what you are getting too?

14. Feb 22, 2015

### PeroK

How did you get that answer?

15. Feb 22, 2015

### goonking

16. Feb 22, 2015

### Staff: Mentor

It's wrong because you didn't integrate.

First step is to convert F(t) to a(t), acceleration as a function of time. Then integrate this a(t) to arrive at v(t).

17. Feb 22, 2015

### goonking

so to convert F(t) to a(t), do you just divide F(t) by the mass 6kg? since F=ma

18. Feb 22, 2015

### Staff: Mentor

Yes, that's it!

19. Feb 22, 2015

### goonking

yes! the answer is 11.63 m/s.
thank you! finally I can move on

20. Feb 22, 2015

### Staff: Mentor

We would appreciate it if you'd type in your working as text, rather than attach a pic. That way we can quote a line that needs attention, as well as it being more legible (usually), and for those using mobile devices the download is faster and far less costly. Please bear that in mind for future postings.

21. Feb 22, 2015

### goonking

I'm not too familiar with posting my work as text. Do I need a program to do that?

22. Feb 22, 2015

### Staff: Mentor

That means you type it on your keyboard as F=ma and v(t)=∫a(t).dt

For more complicated mathematical expressions, you can start to learn Latex.