Unknown Speed for Half Distance – Rankers Physics
Topic: Kinematics
Subtopic: Average Speed and Velocity

Unknown Speed for Half Distance

A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed \( v \). The average speed is 48 km/h. The value of \( v \) is:

(1991)

56 km/h
60 km/h
50 km/h
48 km/h

Solution:

Concept: Average speed for two equal distance segments is \( v_{avg} = \frac{2v_1 v_2}{v_1 + v_2} \). Given \( v_{avg} = 48 \text{ km/h} \), \( v_1 = 40 \text{ km/h} \), and \( v_2 = v \). Substitute these values: \( 48 = \frac{2 \times 40 \times v}{40 + v} \). Simplify and solve for \( v \): \( 48(40+v) = 80v \) leads to \( 32v = 1920 \), so \( v = 60 \text{ km/h} \).

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