question_answer

A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be                         [Pb. PET 2003]

A)              4 m/s             

B)                         2.5 m/s            

C)                         5.5 m/s            

D)                                  11 m/s

Correct Answer: C

Solution :

                \[\because {{S}_{1}}=ut+\frac{1}{2}a{{t}^{2}}\]         .....(i)             and velocity after first t sec             \[v=u+at\]                                                                  Now, \[{{S}_{2}}=vt+\frac{1}{2}a{{t}^{2}}\]             \[=(u+at)t+\frac{1}{2}a{{t}^{2}}\]          ..... (ii)             Equation (ii) ? (i) \[\Rightarrow {{S}_{2}}-{{S}_{1}}=a{{t}^{2}}\]             \[\Rightarrow a=\frac{{{S}_{2}}-{{S}_{1}}}{{{t}^{2}}}=\frac{65-40}{{{(5)}^{2}}}=1\ m/{{s}^{2}}\]             From equation (i), we get,             \[{{S}_{1}}=ut+\frac{1}{2}a{{t}^{2}}\]\[\Rightarrow 40=5u+\frac{1}{2}\times 1\times 25\]             \[\Rightarrow 5u=27.5\] \[\therefore \ \ u=5.5\ m/s\]