# Find Velocity given Force and Mass

1. Mar 17, 2009

### alexas

1. The problem statement, all variables and given/known data

A 4.80 kg object initially at rest at the origin is subjected to the time-varying force shown in the figure

What is the object's velocity at t =6 s ?

2. Relevant equations

F = ma ????????

3. The attempt at a solution

I guessed that the answer was 4.17 m/s (by doing a lot of googling), which was correct but i have no idea how to do this problem if it were on a test.

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2. Mar 17, 2009

### Ofey

Well, There is a formula which states that

$$v=at$$

where v is the final velocity, a is the (average) acceleration and t is the time the body accelerates.

This is a pretty intuitive formula if you think a little bit about it. The acceleration is unknown, but you can express it in terms of F and m (since you know that $$F=ma$$)

Combining these gives

$$v_{final}=\frac{F}{m} t$$

This we can write as

$$v_{final}=\frac{Ft}{m}$$

$$Ft$$ represents the integral (area under the graph) from 0-4 seconds. If/after you study more differential math this will also be intuitive.

Does this help?

Notice that the body doesn't accelerate after 4 seconds, since no force acts on it, and thus its speed stays constant. In other words the body has the same speed at 4 seconds and 6 seconds (if opposing forces are assumed to be small)

Last edited: Mar 17, 2009
3. Mar 17, 2009

### tiny-tim

Hi alexas!

I assume you knew that F = ma, or force = mass times acceleration, and so you could get the acceleration from the graph by dividing by 4.8

ok … draw a new graph (in your mind, if you like) …

it has acceleration against time …

how can you find the velocity just by looking at that graph?