A) 24 m
B) 40 m
C) 56m
D) 16m
Correct Answer: C
Solution :
Key Idea: Velocity is the 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 ie, \[v=\frac{dx}{dt}\] \[\therefore \] \[v=\frac{d}{dt}(40+12t-{{t}^{3}})\] \[=0+12-3{{t}^{2}}\] but final velocity \[v=0\] \[\therefore \] \[12-3{{t}^{2}}=0\] Or \[{{t}^{2}}=\frac{12}{3}=4\] Or \[t=2s\] Hence, distance travelled by the particle before coming to rest is given by \[x=40+12(2)-{{(2)}^{3}}\] \[=40+24-8=64-8\] \[=56m\]
You need to login to perform this action.
You will be redirected in
3 sec
