To determine if an impulse is positive or negative, we need to consider the direction of the net force acting on an object. Impulse is defined as the change in momentum of an object, and momentum is a vector quantity. This means that momentum has both magnitude and direction.

When a force is applied to an object, it can cause the object to speed up, slow down, or change direction. The change in momentum of the object is directly proportional to the force applied and the time over which the force acts. Mathematically, impulse (J) is equal to the force (F) multiplied by the time interval (Δt) over which the force acts:

J = F * Δt

Now, let’s consider a specific scenario to illustrate how we determine the sign of impulse. Suppose you are pushing a box to the right with a force of 50 Newtons for a duration of 2 seconds. In this case, the force and the displacement are in the same direction, so the impulse would be positive.

However, if you were to pull the box to the left with the same force and duration, the force and displacement would be in opposite directions. In this case, the impulse would be negative because the net force is acting in the negative direction.

The sign of impulse depends on the direction of the net force. If the force and displacement are in the same direction, the impulse is positive. If they are in opposite directions, the impulse is negative.

To further clarify, here are some key points:

Positive impulse:

– Force and displacement are in the same direction.

– The object’s momentum increases.

– The object speeds up or changes direction in the same direction as the force applied.

Negative impulse:

– Force and displacement are in opposite directions.

– The object’s momentum decreases.

– The object slows down or changes direction opposite to the force applied.

Remember that impulse is a vector quantity, so it has both magnitude and direction. It is essential to consider the direction of the net force to determine if impulse is positive or negative in a given situation.

I hope this explanation helps clarify how we determine the sign of impulse based on the direction of the net force.