hi, i'm wondering if anyone could explain to me why one uses the following technique to solve this problem.(adsbygoogle = window.adsbygoogle || []).push({});

Let's say we've a 10 kg object. The force exerted on it is

F = 10 + 2t

The force acts on it for two (2) seconds. If it starts at rest, what is the final velocity?

I used this technique to solve the problem, after first making a mistake

dp = F(net) * dt

breaking that down to

dp = (10 + 2t) * dt

integration giving

10t + t^2 from 0 to 2

giving

24 kg * m/s

so

dp = 24 kg * m/s

m(v(2)-v(1)) = 24 kg * m/s

10 kg (v(2)-0) = 24 kg * m/s

v(2) = 2.4 m/s

this is the correct answer, however, initially i tried

m(v(2)-v(1)) = (10 + 2t) * dt

10 kg (v(2)-0) = 14N * 2s

resulting in a velocity of 2.8 m/s

why do i use integration before involving momentum is my question. thanks for anyone who might be able to help!

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# Homework Help: Simple Velocity Problem

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