Velocity Midway in Uniform Acceleration – Rankers Physics
Topic: Kinematics
Subtopic: Equations of Motion

Velocity Midway in Uniform Acceleration

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity \(30\text{ km/h}\) and \(40\text{ km/h}\) respectively. The velocity of the car midway between P and Q is:

(1988)

33.3 km/h
\(20\sqrt{2}\text{ km/h}\)
\(25\sqrt{2}\text{ Km/h}\)
35 km/h

Solution:

Concept: Equations of motion under uniform acceleration.
Formula: \(v^2 = u^2 + 2as\).
Solution: Let \(u_P=30\), \(v_Q=40\) and distance be \(s\). \(v_Q^2 = u_P^2 + 2as\) gives \(40^2 = 30^2 + 2as\) => \(1600 = 900 + 2as\) => \(2as = 700\) => \(as = 350\). For the midway point, \(v_m^2 = u_P^2 + 2a(s/2) = u_P^2 + as = 30^2 + 350 = 900 + 350 = 1250\). So, \(v_m = sqrt{1250} = 25\sqrt{2}\text{ km/h}\).

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