First slide

The 3 equation for uniform acc

Question

A vehicle moving with a constant acceleration from A to B in a straight line AB, has velocities u and v at A and B, respectively. C is the mid-point of AB. If time taken to travel from A to C is twice the time
taken to travel from C to B, then the velocity of the vehicle v at B is

Moderate

A

5 u
B

6 u
C

7 u
D

8 u

Solution

According to question, the given condition can be depicted as
For motion from A to C,
$\frac{s}{2} = 2 u t + \frac{1}{2} a \times (2 t)^{2} = 2 u t + 2 a t^{2}$ …(i)
Also, for motion from C to B,
$\frac{s}{2} = v^{'} t + \frac{1}{2} a t^{2} = (u + 2 a t) t + \frac{1}{2} a t^{2}$
(Let initial velocity be v' = u + 2at)
$= u t + 2 a t^{2} + \frac{1}{2} a t^{2}$
Now, from Eq. (i), we get
$2 u t + 2 a t^{2} = u t + 2 a t^{2} + \frac{1}{2} a t^{2} \Rightarrow u = \frac{a t}{2}$
For overall motion,
$v = u + 3 a t = \frac{a t}{2} + 3 a t = \frac{7 a t}{2} = 7 u (∵ u = \frac{a t}{2})$

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