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The motion of a particle of mass m is given by x=0 for t<0 s, x(t)=A sin 4πt for 0<t<(1/4)s (A>0), and x=0 for t>(1/4) s. Then:

(a) The force at t=(1/8) s on the particle is 16π2Am
(b) The particle is acted upon by an impulse of magnitude 4π2Am at t=0 s and t=(1/4) s
(c) The particle is not acted upon by any force
(d) The particle is not acted upon by a constant force
(e) There is no impulse acting on the particle

Which of the following statement/s is/are true?

1. (a, c, d, e) 2. (a, c)
3. (b, c, d) 4. (a, b, d)
(a, b, d) Hint: Using the equation of position of the particle, we can find the acceleration the particle.
Given,
Step 1: Find the force acting on the particle.
 
a(t)= acceleration =dv(t)dt=16π2Asin4πt At t=18s,a(t)=16π2Asin4π×18=16π2AF=ma(t)=16π2A×m=16π2mA= Change in linear momentum =F×t=(16π2Am)×14=4π2Am
Step 2: Find the impulse of the particle.
The impulse (Change in linear momentum)
                                   at t=0 is same as, t=14s
Clearly, toræ A which is not constant. Hence. force is also not constant.