Average Speed

1. Introduction

Average speed is defined as the total distance travelled divided by the total time taken.
It provides a measure of how fast an object moves overall, regardless of changes in its instantaneous speed.

[\text{Average Speed} ; (v_{avg}) = \dfrac{\text{Total Distance Travelled}}{\text{Total Time Taken}}]

2. SI Unit and Dimensional Formula

SI Unit: [m/s]
Dimensional Formula: [M^0 L^1 T^{-1}]

3. Key Notes

Average speed depends only on distance, not on displacement.
It is always a scalar quantity.
It can never be negative because distance is always non-negative.

4. Practice Questions

Example 1: Single Journey

A car travels 100 km in 2 hours.

[v_{avg} = \dfrac{\text{Total Distance}}{\text{Total Time}} = \dfrac{100, \text{km}}{2, \text{h}} = 50 , \text{km/h}]

Example 2: Two-Leg Journey with Equal Time

A car moves at 60 km/h for 2 hours and then at 40 km/h for another 2 hours.

Total distance travelled:
[d_1 = 60 \times 2 = 120 \text{km}]
[d_2 = 40 \times 2 = 80 \text{km}]
[d_{total} = 120 + 80 = 200 \text{km}]
Total time taken:
[t_{total} = 2 + 2 = 4 \text{h}]
Average speed:
[v_{avg} = \dfrac{200}{4} = 50 \text{km/h}]

Example 3: Two-Leg Journey with Equal Distance

A car covers 60 km at 40 km/h and the next 60 km at 60 km/h.

Time for each leg:
[t_1 = \dfrac{60}{40} = 1.5 , \text{h}, \quad t_2 = \dfrac{60}{60} = 1 \text{h}]
Total distance:
[d_{total} = 60 + 60 = 120 \text{km}]
Total time:
[t_{total} = 1.5 + 1 = 2.5 \text{h}]
Average speed:
[v_{avg} = \dfrac{120}{2.5} = 48 \text{km/h}]

Conceptual Questions

1. Why does average speed differ from instantaneous speed?

Instantaneous speed is measured at a specific moment, whereas average speed considers the whole journey.

2. Is it possible for average speed to be zero? Explain.

Yes, if the total distance travelled is zero — for example, if the object never moved.

3. A cyclist moves 3 km east and 4 km west in 1 hour. Find the average speed.

Total distance = 3 + 4 = 7 km; total time = 1 h ⇒ [v_{avg} = \dfrac{7}{1} = 7 \, \text{km/h}]

4. Can average speed ever be greater than maximum instantaneous speed?

No. The maximum instantaneous speed is the highest speed reached during the journey, so the average cannot exceed it.

5. A runner covers equal distances at two different speeds. How do you calculate the average speed?

For equal distances, [v_{avg} = \dfrac{2v_1v_2}{v_1 + v_2}]

6. If distance is fixed but time varies, what happens to the average speed?

If the distance is fixed and the time decreases, the average speed increases, and vice-versa.

7. Compare average speed in equal-distance vs equal-time cases.

In equal-distance cases, the average speed is the harmonic mean of the two speeds.
In equal-time cases, the average speed is the arithmetic mean of the two speeds.

8. Why is harmonic mean used in average speed calculation when distances are equal?

Because the time for each leg of the journey is inversely proportional to the speed.

9. A car completes a round trip between two cities. Under what condition is average speed equal to the average of the two speeds?

Only when both speeds are equal.

10. Explain why average speed is not affected by the direction of motion.

Average speed depends only on total distance and total time; direction doesn’t affect it.

FAQs / Common Misconceptions

1. Is average speed always equal to the arithmetic mean of the speeds?

No. It equals the arithmetic mean only when the time intervals for each part of the journey are equal.

2. Why can’t we use displacement in place of distance for average speed?

Because average speed is defined using total distance, irrespective of direction.

3. Can average speed be zero if the object moved?

No. As long as distance travelled is non-zero, average speed cannot be zero.

4. Why is average speed not always equal to the average of initial and final speeds?

Because acceleration and time distribution affect the total distance covered at each speed.