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The force applied on a moving object with a mass of #1 kg # on a linear path is given by #F(x)=2x +3#. How much work would it take to move the object over #x in [1,2] #?

Answer 1

Leo Abeyta

#W=10-4=6J#

#W=int_a^b F(x)*d x#

#W=int_1^2(2x+3)d x=|2*x^2/2+3x|_1^2=|x^2+3x|_1^2#

#W=(2^2+3*2)-(1^2+3*1)#

#W=(4+6)-(1+3)#

#W=10-4=6J#

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Answer 2

Charlotte Aaron

To find the work done to move the object over the interval [1, 2], you can use the formula for work: ( W = \int_{1}^{2} F(x) , dx ). Substituting the given force function ( F(x) = 2x + 3 ) into the integral and evaluating it over the interval [1, 2] yields the work done as ( \frac{15}{2} ) joules.

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Answer from HIX Tutor

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.