question_answer

   A particle having initial velocity u is moving with a constant acceleration a for a time t. (i) Find the displacement of the particle in the last 1 s. (ii) Evaluate for u = 2 m/s, a = 1 m/s2 and t = 5 s.

Answer:

                (i) Displacement of a particle at time t, \[s=ut+\frac{1}{2}a{{t}^{2}}\] At time (t -1), displacement of a particle \[s'=u\pm (-1)+\frac{1}{2}a{{(t-1)}^{2}}\]             \[\therefore \] Displacement in the last 1 s is \[{{s}_{t}}=s-s'\] \[=ut+\frac{1}{2}a{{t}^{2}}-\left[ u(t-1)+\frac{1}{2}a{{(t-1)}^{2}} \right]\] \[=ut+\frac{1}{2}a{{t}^{2}}-ut+u-\frac{1}{2}a{{(t-1)}^{2}}\] \[=\frac{1}{2}a{{t}^{2}}+u-\frac{1}{2}a{{t}^{2}}\frac{-a}{2}+at\] \[=u+\frac{a}{2}(1t-1)\] (ii)At \[u=2\,m/s,a=1\,m{{s}^{2}},t=5s\] \[s=2+\frac{1}{2}(10-1)=2+4.5=6.5m\]