Physics Q21 – NEET-UG 2025

Home Physics Motion in a Straight LineQuestion #328

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every

T

min. A girl is driving scooty with a speed of

60

km/h in the direction X to Y notices that a bus goes past her every

30

minutes in the direction of her motion, and every

10

minutes in the opposite direction. Choose the correct option for the period

T

of the bus service and the speed (assumed constant) of the buses.

Clue 1 of 3: Relative Motion

When two objects are moving, their relative speed depends on whether they are moving in the same or opposite directions.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Define variables and relative speeds✦ Active

Let $v_{g}$ be the speed of the girl, which is $60$ km/h. Let $v_{b}$ be the speed of the buses, and $T$ be the time interval (period) between consecutive buses in minutes. The distance between two consecutive buses is $D = v_{b} \times \frac{T}{60}$ km (converting $T$ to hours).

When buses move in the same direction as the girl, the relative speed is $v_{r e l, s a m e} = v_{b} - v_{g}$ . When buses move in the opposite direction to the girl, the relative speed is $v_{r e l, o p p} = v_{b} + v_{g}$ .

Step 2: Formulate equations based on observed time intervals○ Expand

The girl observes a bus every $30$ minutes when moving in the same direction. So, the distance $D$ is covered at the relative speed $v_{r e l, s a m e}$ in $30$ minutes:

D = (v_{b} - v_{g}) \times \frac{30}{60} (1)

The girl observes a bus every $10$ minutes when moving in the opposite direction. So, the distance $D$ is covered at the relative speed $v_{r e l, o p p}$ in $10$ minutes:

D = (v_{b} + v_{g}) \times \frac{10}{60} (2)

Equating (1) and (2) and substituting $v_{g} = 60$ km/h:

(v_{b} - 60) \times 30 = (v_{b} + 60) \times 10

⟹ 3 (v_{b} - 60) = v_{b} + 60

⟹ 3 v_{b} - 180 = v_{b} + 60

⟹ 2 v_{b} = 240

⟹ v_{b} = 120 km/h

💡 Teacher's Secret Hint

Ensure units are consistent (km/h for speed, minutes for time intervals, or convert all to hours).

Step 3: Calculate the bus service period T○ Expand

Now, substitute $v_{b} = 120$ km/h and $v_{g} = 60$ km/h into the expression for $D$ using the definition $D = v_{b} \times \frac{T}{60}$ and one of the relative motion equations, for example, equation (2):

v_{b} \times \frac{T}{60} = (v_{b} + v_{g}) \times \frac{10}{60}

⟹ 120 \times T = (120 + 60) \times 10

⟹ 120 T = 180 \times 10

⟹ 120 T = 1800

⟹ T = \frac{1800}{120} = 15 minutes

Thus, the period $T$ of the bus service is $15$ minutes, and the speed of the buses is $120$ km/h. This corresponds to option (4).

💡 Teacher's Secret Hint

Always double-check your calculations and ensure the final answer matches one of the given options.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 21 – NEET-UG 2025

Clue 1 of 3: Relative Motion

🧠 Full Solution Path