Calculating Impulse and Speed with a Variable Force

In summary, a constant net force expressed as A + Bt^2 is applied to a girl on roller skates in the +x direction. The force starts at t1 = 0 s and continues until t = t2. The expression for the impulse resulting from the applied force is unknown and the expression for the girl's speed at time t2 is also unknown. The question is asking for these expressions.
  • #1
logan9691
2
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A net force given by the expression A + Bt^2, where A and B are constants, is applied to a girl on roller skates in the +x direction. The girl has a mass m. The force starts at t1 = 0 s and continues until t = t2.


Force= A + Bt^2
A and B are constants

I'm not sure how to approach this problem, I haven't had that much experience working with integrals.
 
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  • #3
Oh sorry my bad.

a) what is the expression for the impulse resulting from the applied force?
b) if the girl is initially at rest, what is the expression for her speed at time t2?
 

1. What is the Impulse Force Integral?

The Impulse Force Integral is a mathematical concept used in physics to calculate the change in momentum of an object over a period of time. It is represented by the area under the graph of force vs. time and is measured in Newton-seconds (N·s).

2. How is the Impulse Force Integral calculated?

The Impulse Force Integral is calculated by taking the integral of the force with respect to time. This can be done by using the formula ∫Fdt, where F represents force and t represents time. The resulting value is the change in momentum, which can be used to determine the velocity or displacement of an object.

3. What is the significance of the Impulse Force Integral?

The Impulse Force Integral is significant because it helps us understand the effect of a force on an object over a period of time. It allows us to determine the change in momentum and predict the resulting motion of an object. This concept is crucial in the study of mechanics and is used in various fields such as engineering, sports science, and biomechanics.

4. How does the Impulse Force Integral relate to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the net force acting on an object is equal to its mass multiplied by its acceleration. The Impulse Force Integral allows us to calculate the net force by integrating the applied force over time. By using this integral, we can verify that the net force is indeed equal to the change in momentum, as stated in Newton's Second Law.

5. Can the Impulse Force Integral be negative?

Yes, the Impulse Force Integral can be negative. This occurs when the force acting on an object is in the opposite direction of its initial momentum. In this case, the change in momentum will be negative, indicating a decrease in speed or a change in direction. However, the magnitude of the integral will still represent the total change in momentum, regardless of its direction.

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