Homework Help: Laws of Motion: Force

1. Dec 13, 2004

BbyBlue24

A time-dependent force, F=(8i-4tj) N, where t is in seconds is exerted on a 2 kg object initially at rest. At what time will the object be moving with a speed of 15 m/s?

2. Dec 13, 2004

Pyrrhus

Use Newton's 2nd Law rearranged in this way:

$$\sum_{i=1}^{n} F_{i} = m \frac{dv}{dt}$$

$$\sum_{i=1}^{n} F_{i}dt = mdv$$

3. Dec 13, 2004

BbyBlue24

With this problem I figured the Acceleration = Force/Mass = 4i - 2tj. I tried using the equation velocity = at; 15=4i - 2tj which gives me a false answer and is where I am stuck at. Thanks.

4. Dec 13, 2004

Pyrrhus

Integrate

$v_{o} = 0$

$$\int_{0}^{t} 8 \hat{i} - 4t \hat{j} dt = \int_{0}^{v} m dv$$

Note: Are you on a calculus based course?

5. Dec 13, 2004

BbyBlue24

Yes, a calculus based engineering course.

Last edited: Dec 13, 2004
6. Dec 13, 2004

Pyrrhus

Well, then integrate then substitute for v the value 15 m/s and solve the problem.

7. Dec 13, 2004

BbyBlue24

I am still having problems with this problem; I have a quadratic equation of 15^2=16t^2+4t^4, with the time equal to 2.4, but this is not the correct answer, please help, thanks!

8. Dec 13, 2004

Pyrrhus

That's the answer around 2.4 seconds.

9. Dec 13, 2004

Thank you!