Equations of Motion: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Equations of Motion. Understanding the underlying formula is key to arriving at the correct answer below:

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, \(v_m = sqrt{1250} = 25\sqrt{2}\text{ km/h}\).