Physics Force Question

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A 100N force is applied to a 10 kg object for 2s. If the obj is initially at rest, what is its final velocity. (The angle is 30 degrees, BTW, so cos 30 is 0.87)

 

I know the answer is 17.4 m/s. The problem is I don't get why the method I used didn't work. According to the answer key,

First, find a using F = ma, so a = 8.7 m/s^2. Then using v = v0 + at, so v = 17.4 m/s.

 

I used Fvcos30 = mv^2/(2t), so v = 34.8 m/s. Why does this method not work?

Thanks in advance.

[avenir001]

well it's because your equation Fvcos30 = mv^2/(2t) actually comes from Fdcos30 = mv^2/2 <--- this equation is correct since the work done = the change in kinetic energy (with v being the final velocity of the object).

When u divide both sides by t, you have:

F(d/t)cos30 = mv^2/2t...now, it's true that d/t = velocity but u have to remember that this is referring to average velocity, not final velocity (which is what the v on the right side refers to)...this is because F(d/t)cos30 refers to the force u apply to move the object a certain distance d over a certain period of time t..so d/t is actually the average velocity of the object over that interval...but u know that going from 0 ===> vf, your average velocity will be vf/2...so u can write it like this:

 

F(vf/2)cos30 = mvf^2/2t

 

and now u should get the right answer.

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thanks avenir001.

 

I guess it's safer to use primary velocity formulas for finding instantaneous velocity then.