The force applied against a moving object travelling on a linear path is given by #F(x)= x^2+4x#. How much work would it take to move the object over #x in [0, 4] #?

1 Answer
Sep 18, 2016

Answer:

I found: #53.bar(3)J#

Explanation:

Here I would use the integral definition of work for a variable force as:
#W=int_(x_1)^(x_2)F(x)dx=int_0^4(x^2+4x)dx=#
#=x^3/3+cancel(4)^2x^2/cancel(2)=# evaluated between #0# and #4#:
#=(4^3/3+2*4^2)-0=160/3J=53.bar(3)J#