A) 20 m
B) 18 m
C) 16 m
D) 25 m
Correct Answer: B
Solution :
Given, \[a=\frac{dv}{dt}=6t+5\] or \[dv=(6t+5)\,\,dt\] Integrating, we get \[\int_{0}^{v}{dv=}\int_{0}^{t}{(6t+5)\,\,dt}\] or \[v=\left( \frac{6{{t}^{2}}}{2}+5t \right)\] Again \[v=\frac{ds}{dt}\] \[\therefore \] \[ds=\left( \frac{6{{t}^{2}}}{2}+5t \right)dt\] Integrating again, we get \[\int_{0}^{s}{ds}=\int_{0}^{t}{\left( \frac{6{{t}^{2}}}{2}+5\,t \right)\,\,dt}\] \[\therefore \] \[s=\frac{3\,{{t}^{3}}}{3}+\frac{5\,\,{{t}^{2}}}{2}\] When, \[t=2\,s,\,s=3\times \frac{{{2}^{3}}}{3}+\frac{5\times {{2}^{2}}}{2}\] \[=3\times \frac{8}{3}+\frac{5\times 4}{2}\] = 8 + 10 = 18m
You need to login to perform this action.
You will be redirected in
3 sec
