A) 24 m
B) 40 m
C) 56 m
D) 16 m
Correct Answer: C
Solution :
Key Idea: Velocity is rate of change of distance or displacement. Distance travelled by the particle is \[x=40\,\,+12t-{{t}^{3}}\] We know that, velocity is rate of change of distance i.e., \[v=\frac{dx}{dt}\] \[\therefore v=\frac{d}{dt}(40+12t-{{t}^{3}})\] \[=0+12-3{{t}^{2}}\] but final velocity v = 0 \[\therefore 12-3{{t}^{2}}=0\] \[or{{t}^{2}}=\frac{12}{3}=4\] \[ort=2\,s\] Hence, distance travelled by the particle before coming to rest is given by \[x=40+12(2)-{{(2)}^{3}}\] = 40 + 24 - 8 = 64 - 8 = 56 mYou need to login to perform this action.
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