question_answer

                       Position of a particle moving along x-axis is given by x = 3t - 4t2 + t3, where x is in metres and t in seconds. (i) Find the position of the particle at t = 2 s. (ii)Find the displacement of the particle in the time interval from t = 0 to t = 4 s. (iii) Find the average velocity of the particle in the time interval from t = 2s to t = 4 s

Answer:

                (i) Position of the particle at t = 2 s, then               \[x(2)=3\times 2-4\times {{(2)}^{2}}+{{(2)}^{3}}\] \[=6-4\times 4+8=-2m\]                               \[x(4)=3\times 4-4\times {{(4)}^{2}}+{{(4)}^{3}}=12m\] Displacement \[=x(4)-x(0)=12m\] (iii) \[{{V}_{av}}=\frac{x(4)-x(2)}{4-2}=\frac{12-(-2)}{2}=7\,\text{m/s}\]