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

1 Answer
Oct 9, 2016

Answer:

I found #6.7J#

Explanation:

I think we would need at least an equal force to keep on moving the object as the one opposing it (at least without accelerating it maintaining a constant velocity)..
Here we have a variable force (depending on #x#) so we need to use the integral form for Work as:
#W=int_(x_1)^(x_2)F(x)dx#
or in our case:
#W=int_1^2(2+e^x)dx=#
let us solve it:
#W=2x+e^x# evaluated between #1 and 2# gives us:
#W=(4+e^2)-(2+e)=2+e^2-e=2+e(e-1)=6.67~~6.7J#