Physics Q17 – NEET-UG 2023

Home Physics Motion in a Straight LineQuestion #330

A vehicle travels half the distance with speed

ϑ

and the remaining distance with speed

2 ϑ

. Its average speed is:

Clue 1 of 3: Definition of Average Speed

Average speed is defined as the total distance covered divided by the total time taken.

🥷

Ninja Strategy•Range Analysis

The average speed must always lie between the minimum and maximum speeds encountered during the journey. By checking which options fall within the range $[ϑ, 2 ϑ]$ , one can quickly identify the correct answer.

🧠 Full Solution Path

Step 1: Define Variables and Calculate Time for Each Segment✦ Active

Let the total distance traveled by the vehicle be $D$ . The vehicle travels half the distance, which is $\frac{D}{2}$ , with speed $ϑ$ . The time taken for this first half is $t_{1} = \frac{distance}{speed} = \frac{D / 2}{ϑ} = \frac{D}{2 ϑ}$ .

The remaining distance is also $\frac{D}{2}$ , and it is covered with speed $2 ϑ$ . The time taken for this second half is $t_{2} = \frac{distance}{speed} = \frac{D / 2}{2 ϑ} = \frac{D}{4 ϑ}$ .

Step 2: Calculate Total Distance and Total Time○ Expand

The total distance traveled is $D$ .

The total time taken is the sum of the times for each segment: $T = t_{1} + t_{2}$ .

T = \frac{D}{2 ϑ} + \frac{D}{4 ϑ} = \frac{2 D + D}{4 ϑ} = \frac{3 D}{4 ϑ}

💡 Teacher's Secret Hint

Ensure common denominators when adding fractions.

Step 3: Calculate Average Speed○ Expand

The average speed is defined as the total distance divided by the total time.

Average Speed = \frac{Total Distance}{Total Time} = \frac{D}{\frac{3 D}{4 ϑ}}

Simplifying the expression:

Average Speed = D \times \frac{4 ϑ}{3 D} = \frac{4 ϑ}{3}

💡 Teacher's Secret Hint

The total distance $D$ cancels out, as expected for average speed problems where distances are given in terms of fractions of total distance.

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Physics Question 17 – NEET-UG 2023

Clue 1 of 3: Definition of Average Speed

🧠 Full Solution Path