A vehicle travels 4 km with a speed of 3 km/h and another 4 km with a speed of 5 km/h, then its average speed is:

Given: The vehicle travels two equal distances of 4 km each with speeds 3 km/h and 5 km/h. Find: The average speed. From the solution: Vav2 = 13 + 15 = 158 Hence, Vav = 415 = 3.75 km/h Therefore, the average speed is 3.75 km/h. The solution states the correct option is A.

A vehicle travels 4 km with a speed of 3 km/h and another 4 km wi… — Solution | JEE Physics

MCQEasyJEE 2023Velocity & Acceleration

A vehicle travels $4 \, \text{km}$ with a speed of $3 \, \text{km/h}$ and another $4 \, \text{km}$ with a speed of $5 \, \text{km/h}$ , then its average speed is:

A
$4.25 \, \text{km/h}$
B
$3.50 \, \text{km/h}$
C
$4.00 \, \text{km/h}$
D
$3.75 \, \text{km/h}$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The vehicle travels two equal distances of $4 \, \text{km}$ each with speeds $3 \, \text{km/h}$ and $5 \, \text{km/h}$ .

Find: The average speed.

From the solution:

\frac{V_{av}}{2} = \frac{1}{3} + \frac{1}{5} = \frac{15}{8}

Hence,

V_{av} = \frac{4}{15} = 3.75 \, \text{km/h}

Therefore, the average speed is $3.75 \, \text{km/h}$ . The solution states the correct option is A.

Common mistakes

Using the arithmetic mean of the two speeds, $\frac{3+5}{2}$ , is wrong because the average speed must be based on total distance divided by total time. For unequal times, do not average speeds directly.
Ignoring that the two distances are equal can lead to an incorrect method. For equal-distance segments, first compute the time taken in each segment and then use total distance over total time.

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Answer

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