The figure gives the acceleration of a 5.0 kg particle as an applied force moves
ID: 1639144 • Letter: T
Question
The figure gives the acceleration of a 5.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by a_s = 6.0 m/s^2. How much work has the force done on the Particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed and direction (give positive answer if the particle moves along x axis in positive direction and negative otherwise) of travel when it reaches (d) x = 4.0 m, (e) x = 7.0 m, and (f) x = 9.0 m?Explanation / Answer
Work done = Area under the graph*mass
a) W1 = 0.5(3+4)*6*5 = 105 J
b) W2 = 0.5(3+5)*6*5 - 0.5(2+1)*6*5 = 75 J
c) W3 = 0.5(3+5)*6*5 - 0.5(2+4)*6*5 = 30 J
velocity
v^2 = u^2 + 2ax
d) v^2 = 0 + 2*21
v = 6.48 m/s
e) v^2 = 2*15
v = 5.48 m/s
f) v^2 = 0+2*6
v = 3.46 m/s