A force acting on a 1.0-kg object is described by the equation F = (2.0x3.5) i N. (a) Plo the force as a function of x from x = 0 to x = 2.0 m. (b) Use your plot to determine the work do by this force when the object is moved from x = 1.0 to x=2.0 m. (c) Now, integrate W = f F . dr to find this quantity. (d) Are your answers from (b) and (c) the same or differen and why?

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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A force acting on a 1.0-kg object is described by the equation \( \vec{F} = (2.0x - 3.5) \hat{i} \ \text{N} \). 

**(a)** Plot the force as a function of \( x \) from \( x = 0 \) to \( x = 2.0 \ \text{m} \).

**(b)** Use your plot to determine the work done by this force when the object is moved from \( x = 1.0 \) to \( x = 2.0 \ \text{m} \).

**(c)** Now, integrate 
\[ W = \int \vec{F} \cdot d\vec{r} \]
to find this quantity.

**(d)** Are your answers from (b) and (c) the same or different, and why?
Transcribed Image Text:A force acting on a 1.0-kg object is described by the equation \( \vec{F} = (2.0x - 3.5) \hat{i} \ \text{N} \). **(a)** Plot the force as a function of \( x \) from \( x = 0 \) to \( x = 2.0 \ \text{m} \). **(b)** Use your plot to determine the work done by this force when the object is moved from \( x = 1.0 \) to \( x = 2.0 \ \text{m} \). **(c)** Now, integrate \[ W = \int \vec{F} \cdot d\vec{r} \] to find this quantity. **(d)** Are your answers from (b) and (c) the same or different, and why?
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