Physics problem please help!!
A 2.10 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as F = 3x^2 - 2x. If the block's speed passing through the origin was 5.50 m/s, with what speed (in meters/second) does it pass the point x = 8.00 m?

Question

Physics problem please help!!
A 2.10 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as F = 3x^2 - 2x. If the block's speed passing through the origin was 5.50 m/s, with what speed (in meters/second) does it pass the point x = 8.00 m?

anonymous · Answer

Calculate the area under the curve.

irishboy123 · Answer

first, i would plot the curve.  that is *always* a good idea, even if you believe it adds nothing to the final analysis.  you will see that it dips under the x axis, namely the block slows down before it accelerates again.

the area under the curve will equal the work done on the block because W = ∫ F dx. here, interval: 0≤x≤8m.  add the work done to the initial kinetic energy of the block and you can then calculate it's energy after x = 8m. the bit of the work that lies under the curve will net out.