Question

A particle moving with uniform acceleration along
X-axis crosses the points x = 2 m and x = 7 m with
velocities 5 ms-1 and 15 ms-1 respectively. The
velocity with which it crosses point x = 3 m is
(1) root65 ms-1
(2) 10 ms-1
(3)root35​

Answer 1

let initial velocity is u and uniform acceleration is a.

at x = 2m, v = 5m/s

using formula, v² = u² + 2as

⇒(5)² = u² + 2a(2)

⇒25 = u² + 4a..........(1)

at x = 7m , v = 15m/s

so, (15)² = u² + 2a(7)

⇒225 = u² + 14a .........(2)

from equations (1) and (2),

we get, 225 - 25 = 14a - 4a

⇒200 = 10a

⇒a = 20m/s²

and u² = 225 - 14 × 20 = 225 - 280 = -55 m/s

now, velocity at x = 3m, v² = (-55) + 2(20)(3)

= -55 + 120

= 65

so, v = √65 m/s

hence, option (1) is correct choice.

Answer 2

$\huge\bold\purple{Answer:-}$

(1) root65 ms-1