When Should Integrals Be Applied in Physics Problems?

[Will55]

Homework Statement

A crate of mass 9.6 kg is pulled up a rough incline with an initial speed of 1.44 m/s. The pulling force is 92 N parallel to the incline, which makes an angle of 19.4° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.92 m.

(d) What is the change in kinetic energy of the crate?

Homework Equations

Ke_i = 1/2mv²

The Attempt at a Solution

[m(u)^2] / 2
K.E (i) = [9.6(1.44)^2 ] / 2
K.E (i) = 9.95 J

I understand this much is correct. But when and why do I use integrals. I understand it calculates the area under the equation giving me the total amount of work. What I don't understand is, when's the proper time to use it. Are there key words to look out for or...??

 

[Dick]

Homework Statement

A crate of mass 9.6 kg is pulled up a rough incline with an initial speed of 1.44 m/s. The pulling force is 92 N parallel to the incline, which makes an angle of 19.4° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.92 m.

(d) What is the change in kinetic energy of the crate?

Homework Equations

Ke_i = 1/2mv²

The Attempt at a Solution

[m(u)^2] / 2
K.E (i) = [9.6(1.44)^2 ] / 2
K.E (i) = 9.95 J

I understand this much is correct. But when and why do I use integrals. I understand it calculates the area under the equation giving me the total amount of work. What I don't understand is, when's the proper time to use it. Are there key words to look out for or...??

You certainly don't use it here. The crate has a constant velocity, the kinetic energy doesn't change. If the force on the object were variable then you would use the integral of the force over the distance to find the work done by the force on the object. This isn't a good example for that.