The force applied against a moving object travelling on a linear path is given by #F(x)=3x+e^x #. How much work would it take to move the object over #x in [0, 3 ] #?
The work
By signing up, you agree to our Terms of Service and Privacy Policy
To find the work done, integrate the force function ( F(x) ) over the given interval [0, 3]:
[ \text{Work} = \int_{0}^{3} F(x) , dx = \int_{0}^{3} (3x + e^x) , dx ]
Integrate ( 3x ) and ( e^x ) separately:
[ \int_{0}^{3} 3x , dx = \left[\frac{3}{2}x^2\right]{0}^{3} = \frac{9}{2} ] [ \int{0}^{3} e^x , dx = \left[e^x\right]_{0}^{3} = e^3 - 1 ]
Summing up the two integrals:
[ \text{Work} = \frac{9}{2} + (e^3 - 1) ]
Therefore, the work done to move the object over ( x ) in the interval [0, 3] is ( \frac{9}{2} + (e^3 - 1) ).
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.
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.
- What energy transformations takes place in a motor?
- A ball with a mass of #450 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #12 (kg)/s^2# and was compressed by #4/3 m# when the ball was released. How high will the ball go?
- An object with a mass of #2 kg# is hanging from an axle with a radius of #3 m#. If the wheel attached to the axle has a radius of #3 m#, how much force must be applied to the wheel to keep the object from falling?
- How much work would it take to push a # 1 kg # weight up a # 3m # plane that is at an incline of # pi / 4 #?
- Clarification on universal gravitational potential energy re: planet orbiting a star?

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