question_answer

A particle starting from rest from 0 accelerates uniformly along a straight line and in 2 s crosses two points A and B, which are 5 m apart. If velocity at B is 2 m/s more than the velocity at A, find the distance OA.

Answer:

  In AB, \[u+2=u+a\times 2\Rightarrow u+2=u+2a\] \[\Rightarrow a=1m/{{s}^{2}}\] Also, \[5=u\times 2+\frac{1}{2}a\times 4\Rightarrow 5=2u\times 2a\] \[\Rightarrow 5=2u+2\Rightarrow u=\frac{3}{2}m/s\] In OA, \[{{\left( \frac{3}{2} \right)}^{2}}=2\times 1\times s\Rightarrow s=\frac{9}{8}m\]