Question

a body moving with a uniform acceleration had velocities of 20 m/s and 30 m/s when passing the points P and Q of its path. find the velocity midway between P and Q (in m/s)

Answer 1

25.5 m/s is the right answer

Answer 2

Answer:

$\sqrt{650}$

Explanation:

Let acceleration be a, and the distance between P and Q be s.

So,  using equation of motion

$V^{2}$ = $U^{2}$ + 2as

$30^{2}$ = $20^{2}$ + 2a(s/2)

as = 250

Solving, we get: as = 250.

Now, when calculating the velocity at the point midway, we'll take the distance to be s/2, with the same acceleration, and initial velocity 20 m/s (or final 30 m/s, but that one was simpler).

Applying the equation of motion:

$V^{2}$ = $u^{2}$ + 2as

Using as = 250:

V square = 20 square + 250

V square = 650

And, v = $\sqrt{650}$ m/s, which is a scary number.

Properly, v = 25.495 m/s.