What is the Impact of a Time-Dependent Force on an Object's Velocity?

[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?

 

[Pyrrhus]

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

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

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

 

[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.

 

[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?

 

[BbyBlue24]

Yes, a calculus based engineering course.

 

[Pyrrhus]

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

 

[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!

 

[Pyrrhus]

That's the answer around 2.4 seconds.

 

[BbyBlue24]

Thank you!