# The force applied against an object moving horizontally on a linear path is described by #F(x)=xe^x+ 1/x #. By how much does the object's kinetic energy change as the object moves from # x in [ 1, 3 ]#?

Approximately:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the change in kinetic energy as the object moves from ( x = 1 ) to ( x = 3 ), you can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

The work done by the force ( F(x) ) over the interval ( [1, 3] ) is given by the definite integral of ( F(x) ) with respect to ( x ) over that interval:

[ \text{Work} = \int_{1}^{3} F(x) , dx ]

Then, the change in kinetic energy is equal to the work done:

[ \Delta KE = \text{Work} ]

[ \Delta KE = \int_{1}^{3} (xe^x + \frac{1}{x}) , dx ]

[ \Delta KE = \left[ \frac{xe^x}{2} + \ln|x| \right]_{1}^{3} ]

[ \Delta KE ≈ 14.812 , \text{J} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If a strong man lifts a barbell with a mass of 125.7 g and does 5023 joules of work, how high did he lift it?
- An object with a mass of #5 kg# is hanging from an axle with a radius of #18 cm#. If the wheel attached to the axle has a radius of #42 cm#, how much work would it take to turn the wheel #9 cm#?
- If an object with a mass of #7 kg # changes speed from #4ms^-1# to # 5 ms^-1#, by how much does its kinetic energy change?
- An object with a mass of #24 kg# is hanging from an axle with a radius of #4 m#. If the wheel attached to the axle has a radius of #20 m#, how much force must be applied to the wheel to keep the object from falling?
- P=25 watts W=5000 Joules t=? Formula=____________ Substitution=____________ Answer with unit of measure=__________

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7