A force on a particle of 30 grams is acting in such a way that the position of the particle relative to time is given below. x = 3t - 4t2 + t3 where x is in meters and t is in seconds. The work done in the first 4 seconds will be:
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HELLO!!!!
Differentiate the function,
x=t^3-4t^2+2t
dx/dt=v=3t^2-8t+2,
and differentiate it again to get the acceleration.
d^2x/dt^2=a=6t-8
Therefore,
A=6t-8 m/s^2
F=ma,
F=30×10^-3 (6t-8)
At t=4,
F=30 ×10^-3(24-8)=30×10^-3×16
F=48×10^-3
Therefore work done would be,
Work=Force×distance
Distance travelled at t=4,
X=3(4)-4(4)^2+(4)^3
X=12-64+64=12m
Work =48×10^-3×12
W=576×10^-3 J
Hope you get it,
Best of luck!!
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