question_answer

If initial velocity of a particle is u (at t = 0) and the acceleration\[f\]is at, then

A) \[v=u+a{{t}^{2}}\]        

B)         \[v=u+\frac{a{{t}^{2}}}{2}\]  

C) \[v=u+at\]                         

D)  \[v=u\]

Correct Answer: B

Solution :

 Acceleration\[=at\] Increase in velocity             = Area of \[\Delta OAB\]             \[=\frac{1}{2}\times at\times t\]             \[=\frac{1}{2}a{{t}^{2}}\] \[\therefore \]      \[v=u+\frac{1}{2}a{{t}^{2}}\]