A) \[{{T}_{1}}={{T}_{2}}\]
B) \[{{T}_{1}}>{{T}_{2}}\]
C) \[{{T}_{2}}>{{T}_{1}}\]
D) Can?t predicted
Correct Answer: C
Solution :
[c] Acceleration = bt \[a=\frac{dv}{dt}=bt\] \[dv=bt\,dt\] \[\therefore \] Acceleration depends on time so we unable to apply kinematics equation Integrating above equation \[\int\limits_{{{V}_{o}}}^{{{V}_{f}}}{V}=\frac{b{{t}^{2}}}{2}\] \[{{V}_{f}}-{{V}_{o}}=\frac{b{{t}^{2}}}{2}\] \[{{V}_{f}}={{V}_{o}}+\frac{b{{t}^{2}}}{2}\] Again integrate to have distance \[{{V}_{f}}=\frac{dx}{dt}={{V}_{o}}+\frac{1}{2}b{{t}^{2}}\] \[dx=\int{{{V}_{o}}dt}+\int\limits_{o}^{t}{\frac{1}{2}b{{t}^{2}}}dt\] \[x={{V}_{o}}t+\frac{1}{2}\frac{b{{t}^{3}}}{3}\] \[x={{V}_{o}}t+\frac{1}{2}b{{t}^{3}}\]
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