A point moving with constant acceleration from A to B in the straight line AB has velocities u and v at and B respectively. Find its velocity at C, the mid point of AB. Also show that if the time from A to C is twice that from C to B, then `v =7 u`.

Options

A. 5 u
B. 6 u
C. 7 u
D. 8 u

Answer

C

Explanation

According to question, the diagram can be drawn as

For motion from A to C
`(s)/(2)= ut+(1)/(2)a xx(2t)^(2)=2ut+2at^(2)`
Also, for motion from C to B. (Let initial velocity be `upsilon'`)
`(s)/(2)=(u+2at)t+(!)/(2)at^(2) " " (therefore upsilon' = u+2at)`
`=ut+2at^(2)+(1)/(2)at^(2)`
Now, `2ut+2qat^(2)=ut+2at^(2)+(1)/(2)at^(2)rArr u=(at)/(2)`
For overall motion,
`upsilon=u+3at=(at)/(2)+3at=(7at)/(2)=7u " " (therefore u=(at)/(2))`