question_answer

A body moving with uniform acceleration covers 100 m in the first 10 seconds and 150 m in the next 10 seconds. What is the initial velocity of the body?

Answer:

Let u and a respectively be the initial velocity and acceleration of the body. From\[S=ut+\frac{1}{2}a{{t}^{2}}\] \[100=10\times u+\frac{1}{2}\times a\times {{(10)}^{2}}\] \[100=10u+50a\] \[\Rightarrow u+5a=10\]                                              ……..(1) \[250=20u+100a\] \[u+10a=12.5\]                                 ………(2) Multiplying equation (1) by (2), we get, \[2u+10a=20\]                                   ………(3) On solving equations (2) and (3) \[u=7.5m{{s}^{-1}}\] \[\therefore \]Initial velocity of the body\[=7.5m{{s}^{-1}}\]