Figure 7-39 gives the acceleration of a 1.75 kg particle as it is moved from res

Question

Figure 7-39 gives the acceleration of a 1.75 kg particle as it is moved from rest along an x axis by an applied force Fa, from x = 0 to x = 9 m.

How much work has the force done on the particle when the particle reaches the following points?

(a) x = 4 m J

(b) x = 7 m J

(c) x = 9 m J

What is the particle's speed and direction of travel when it reaches each of the following points?

(d) x = 4 m m/s

(e) x = 7 m m/s

(f) x = 9 m m/s

Explanation / Answer

workdone = integral Fdx =>integral of madx =>integral is nothing but area of the graph (a) x = 4 m =>(area upto x=4)*m =>1.75(1/2*6*1 + 3*6 + 1/2*1*6 ) =>42 J (b) x = 7 m =>area upto 7 *m =>1.75(24 - 1/2*1*6 ) =>36.75 J (c) x = 9 m =>area upto 9 =>1.75(24 - (1/2*1*6 +2*2 + 1/2*1*6)) =>24.5 J (d) x = 4 m wordone = change in KE =>1/2mv^2=42 =>v= 6.92 m/s (e) x = 7 m wordone = change in KE =>1/2mv^2=36.75 =>v= 6.48 m/s (f) x = 9 m wordone = change in KE =>1/2mv^2=24.5 =>v= 5.29 m/s

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