Posted by **Hope** on Wednesday, December 2, 2009 at 6:15am.

A 1.6 kg particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.2 m/s at x = 0 m.

The figure or graph has F (N) along the y axis and velocity along the x axis. A diagonal line drops from positive 10 force to -10 force from 0 cm to 4 cm. and crosses the x axis at 2 cm.

What is its velocity at 2 cm and 4 cm?

What formula do I need to use?

physics - drwls, Tuesday, December 1, 2009 at 6:58pm

Integrate F dx from 0 to 0.02 m to get the change in kinetic energy (KE) at 2 cm. Use the new value of the KE to get the new velocity. Then do it again for 0.02 to 0.04 m. The KE will decrease, since the force on the particle is in the opposite direction to motion over that interval.

physics - Hope, Tuesday, December 1, 2009 at 10:20pm

Please explain to me how to integrate-I am unsure exactly what this means in this problem

Thanks

- physics -
**bobpursley**, Wednesday, December 2, 2009 at 8:38am
Ok, integrate is a calculus term. Here is the algebra way.

You know f(x)*x is the energy. But f(x)*x is the area under the f(x) line. So use your geometry to find the area under the f(x) line first at x=.02m, then x=.04 m.

That area is the energy gained.

KEfinal=keoriginal+ energy gained.

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