# Calculating Velocity After 2s of Force on 10kg Mass

• watsup91749
In summary, the force exerted on a 10kg mass is given by F=10 + 2t and the units are SI. If the mass starts from rest, its velocity after 2s can be found by either using the average acceleration or by integrating the force equation and solving for velocity. The two methods result in the same answer, which is 2.4 m/s.
watsup91749

## Homework Statement

The force exerted on a 10kg mass is given by F=10 + 2t where the units are SI. If the mass starts from rest, its velocity after 2s is:
A) 14 m/s
B) 2 m/s
C) 2.4 m/s
D) .2 m/s
E) .24 KM/S

F=ma
thats it?

## The Attempt at a Solution

At 2 secs the force would be 14 N so..well, I am not sure on what to do. i could probably figure it out if i knew what i was supposed to do though. I am not sure how a varying force could be ...i have no idea what I am talking about :(. Any help would be greatly appriciated.

Well, you know the mass, so you can find the acceleration of the object. You can probably use a kinematics equation that will tell you it's velocity after 2 seconds. (remember it starts at rest.

if you mean like v(f)=v(i) + at, then i can't use that because i don't have the acceleration or the final velocity, the force that acts on it is external so...am i confusing my self here?

Well you found the force at t=2 which is F=14...and F=ma...you can find acceleration now...

OK, the probelm with this question is the variable force.

The way I see this there are two ways to solve it. One is easy, one is harder.

The easy way is to notice that the force increases linearly with time, therefore you can find the average acceleration and simply use that in the F = ma equation. As you are looking at a period of 2 seconds, and the average occurs mid-way between 0 seconds and 2 seconds, I'll let you take it from here.

The harder way is to integrate F = 10 + 2t with respect to t. For which you get Ft = 10t + t^2, since Ft (Force * time) is an impulse, you can then use Ft = mv to come to your answer. 10t + t^2 = m * v, and solve for v where m = 10 and t = 2.

you guys are awesome, thanks a ton :D

Ah, I did my integration a bit hurridly, what I should have said was:
$$Ft = 10t + t^{2} + c$$

Then when t = 0:
$$0 = 0 + 0 + c$$
Therefore:
$$c = 0$$
Therefore:
$$Ft = 10t + t^{2}$$

## What is velocity?

Velocity is a measure of the rate of change of an object's position over time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## How do you calculate velocity?

Velocity is calculated by dividing the change in an object's position by the time it took for that change to occur. In other words, velocity = displacement/time.

## What is the formula for calculating velocity?

The formula for calculating velocity is v = Δx/Δt, where v is velocity, Δx is the change in position, and Δt is the change in time.

## How do you calculate velocity after 2 seconds of force on a 10kg mass?

To calculate velocity after 2 seconds of force on a 10kg mass, you would need to know the initial velocity, the acceleration of the object, and the time. The formula would be v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

## What is the unit of measurement for velocity?

The unit of measurement for velocity is meters per second (m/s). This is a combination of the unit for distance (meters) and the unit for time (seconds).

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