# Impulse/final velocity question confusion

• student07
In summary, impulse and final velocity are related through the impulse-momentum theorem and the magnitude of impulse is directly proportional to the change in final velocity. Impulse and final velocity are two different physical quantities, with impulse measuring the change in momentum and final velocity measuring the speed and direction of an object after the impulse is applied. The mass of an object does not directly affect its final velocity, but a larger mass will require a greater impulse to produce the same change in momentum. An object can have a final velocity without an impulse, but an impulse is necessary to change the velocity of a stationary object. The direction of an impulse affects the final velocity of an object, with a same-direction impulse increasing the final velocity and an opposite-direction impulse decreasing it
student07
I uploaded my question below; basically I am confused in part b) where they show that:
50 kgm/s = (5kg)v2 - (5kg)(-4m/s) then they say that
30 kgm/s = 5kg v2, but shouldn't it be 70 kgm/s = 5kg v2?

As noted at the beginning of the question North is positive and thus since the cart moves south is negative (-4m/s).
Could this be a typo ?

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If south is negative and that was the initial direction of momentum then the second term is written correctly. Note carefully the signs (subtracting a negative on the RHS) so the second line is correct because the equation reads (without units) 50 = 5v + 20.

yeah I totally missed the subtracting a negative on the RHS that makes more sense now thank you

## 1. How are impulse and final velocity related?

Impulse and final velocity are related through the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse applied to it. This means that the magnitude of the impulse applied to an object is directly proportional to the change in its final velocity.

## 2. What is the difference between impulse and final velocity?

Impulse and final velocity are two different physical quantities. Impulse is a measure of the change in an object's momentum, while final velocity is the speed and direction at which the object is moving after the impulse has been applied.

## 3. How does the mass of an object affect its final velocity?

The mass of an object does not directly affect its final velocity. However, a larger mass will require a greater impulse to produce the same change in momentum as a smaller mass. This means that a larger mass will have a smaller final velocity compared to a smaller mass when the same amount of impulse is applied.

## 4. Can an object have a final velocity without an impulse?

Yes, an object can have a final velocity without an impulse if it is already in motion or if the impulse was applied over a longer period of time, resulting in a smaller change in velocity. However, an impulse is required to change the velocity of a stationary object.

## 5. How does the direction of an impulse affect the final velocity of an object?

The direction of an impulse is important in determining the direction of the final velocity of an object. If the impulse is applied in the same direction as the object's initial velocity, the final velocity will increase. However, if the impulse is applied in the opposite direction, the final velocity will decrease. If the impulse is applied at an angle to the object's initial velocity, the final velocity will have both a change in magnitude and direction.

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