Find Velocity given Force and Mass

[alexas]

Homework Statement

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 ?

Homework Equations

F = ma ?

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.

 

[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)

 

[tiny-tim]

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 ?
…
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.

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?

 

[Greg Bernhardt]

Velocity is the speed at which an object is moving. It can also be thought of as the speed of a moving object divided by the time of travel. In this case, it is the speed of a body divided by the time taken for the body to move a given distance. This can be expressed mathematically as: v = v 0 t $${\displaystyle v=v_{0}t}$$ where: v = velocity ( m / s or km / h ) v 0 = initial velocity ( m / s or km / h ) t = time ( s or h ) v = final velocity ( m / s or km / h )