Question:
A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is
A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is
Updated On: Apr 29, 2024
- 40 km/h
- 48 km/h
- 50 km/h
- 60 km/h
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The Correct Option is B
Solution and Explanation
Let's consider, \(x =\) total distance covered by the car, Time taken to complete the half distance with velocity \(v =40\, km / h\),
\(t _{1}=\frac{ x }{2 \times 40}=\frac{ x }{80} hr \ldots . .(1)\)
The time taken to complete another half distance with velocity \(u =60 km / h\)
\(t _{2}=\frac{ x }{2 \times 60}=\frac{ x }{120} h\)
The total time taken, \(t = t _{1}+ t _{2}\)
\(t =\frac{ x }{80}+\frac{ x }{120}=\frac{ x }{48} h\)
The average speed of the car,
\(v_{\text{avg}} = \frac{x}{\frac{x}{48}} = 48 \text{ km/h}\)
\(t _{1}=\frac{ x }{2 \times 40}=\frac{ x }{80} hr \ldots . .(1)\)
The time taken to complete another half distance with velocity \(u =60 km / h\)
\(t _{2}=\frac{ x }{2 \times 60}=\frac{ x }{120} h\)
The total time taken, \(t = t _{1}+ t _{2}\)
\(t =\frac{ x }{80}+\frac{ x }{120}=\frac{ x }{48} h\)
The average speed of the car,
\(v_{\text{avg}} = \frac{x}{\frac{x}{48}} = 48 \text{ km/h}\)
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.