A) 576mJ
B) 450mJ
C) 490mJ
D) 530mJ
Correct Answer: A
Solution :
[a] \[\operatorname{x}=3t-4{{t}^{2}}+{{t}^{3}}=\frac{dx}{dt}=3-8\operatorname{t}+3{{t}^{2}}\] Acceleration \[=\frac{{{d}^{2}}x}{d{{t}^{2}}}=-8+6t\] Acceleration after \[4 sec = -8 + 6\times 4 =16 m{{s}^{-2}}\] Displacement in \[4 sec =3\times 4-4\times {{4}^{2}}+{{4}^{3}}=12m\] \[\therefore \] Work = Force \[\times \] displacement \[=Mass\times acc.\times disp.=3\times 1{{0}^{-3}}\times 16\times 12=576mJ\]
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