question_answer

A particle experiences a constant acceleration for 20 seconds after starting from rest. If it travels a distance \[{{s}_{1}}\]in the first 10 seconds and distance \[{{s}_{2}}\]in the next 10 seconds, find the relation between\[{{s}_{1}}\]and\[{{s}_{2}}\].

Answer:

Let a be constant acceleration and \[S=ut+\frac{1}{2}a{{t}^{2}},\]then \[{{S}_{1}}=0+\frac{1}{2}a\times 100=50a\] Velocity after 10s, is \[v=0+10a\] So, \[{{S}_{2}}=10a\times 10+\frac{1}{2}a\times 100=50a\] \[\Rightarrow {{S}_{2}}=3{{S}_{1}}\]