The figure gives the acceleration of a 5.0 kg particle as an applied force moves
ID: 1544445 • 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 as = 6.0 m/s2. 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?
x (m) 0 (6s/tu)oExplanation / Answer
m = 5 kg ; a = 6 m/s^2 ;
(a)x = 4 m
we know that work done is
W = F x d
W = m a d = m (a x d)
Area under the graph for x = 0 to x = 4
W = 5 [1/2 x 6 x 1 + 6 x 3 ] = 105 J
W = 105 J
b)x = 7 m
W = 5 [ 2 x 1/2 x 6 x 1 + 6 x 3 - 1/2 x 6 x 1 - 6 x 2] = 9 J
W = 9 J
c)x = 9 m
W = 5 [ 2 x 1/2 x 6 x 1 + 6 x 3 - 2 x 1/2 x 6 x 1 - 6 x 2] = 6 J
W = 6 J
d)work at x = 4 is
W = 105 J
1/2 m v^2 = 105
v = sqrt (2 x 105/5) = 6.48 m/s
Hence, v = 6.48 m/s