The force ⃗F=F̂i on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x=0. What is the kinetic energy of the particle at x=8 m?

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(4) 29.5 J. Initial kinetic energy: 1/2×2×25=25 J. Signed area: 0 to 2 m, triangle +1/2(2)(2)=2 J; 2 to 3 m, -1/2(1)(1)=-0.5 J; 3 to 4 m, -1 J; 4 to 5 m, -0.5 J; 5 to 8 m, +1/2(3)(3)=4.5 J. Total work =2-0.5-1-0.5+4.5=4.5 J. K=25+4.5=29.5 J.

The force ⃗F=F̂i on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x=0. What is the kinetic energy of the particle at x=8 m?

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