ANAND CLASSES study material and notes boost your JEE, NEET, and CBSE Class 11 exam preparation with these MCQs on Average Speed. Each question includes step-by-step solutions and explanations to help you master this fundamental physics concept.
Average Speed
While travelling in a car (or a bus) we have noticed that it is very difficult to keep the speed of the car at a constant or uniform value because at many places the brakes are to be applied to slow down or stop the car due to various reasons. Thus, the speed of a body is usually not constant and the
distance travelled divided by time gives us the average speed during that time.
Definition :
The average speed of a body for a given interval of time is defined as the ratio of the total distance traveled to the total time taken.
Mathematically,
$$v_{av} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}$$
Understanding Average Speed with an Example
Imagine a car travels 120 km in 3 hours and then another 180 km in 2 hours. The total distance traveled is: 120+180=300 km
The total time taken is: 3+2=5 hours
Thus, the average speed is: $$v_{av} = \frac{300}{5} = 60 \text{ km/h}$$
This means the car covered an average of 60 km per hour over the entire journey.
Types of Average Speed
1. Time-Averaged Speed
When a particle moves at different uniform speeds $v_1, v_2, v_3, \dots$ for different time intervals $t_1, t_2, t_3, \dots$, then:
$$v_{av} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}$$
$$v_{av} = \frac{d_1 + d_2 + d_3 + \dots}{t_1 + t_2 + t_3 + \dots}$$
$$v_{av} = \frac{v_1t_1 + v_2t_2 + v_3t_3 + \dots}{t_1 + t_2 + t_3 + \dots}$$
Example: A bus moves at 40 km/h for 2 hours, then at 60 km/h for 3 hours. What is the average speed of bus ?
Solution :
The total distance traveled: (40×2)+(60×3)=80+180=260 km
Total time taken: 2+3=5 hours
So, the average speed: $$v_{av} = \frac{260}{5} = 52 \text{ km/h}$$
Special Case:
If a particle moves with speed $v_1$ for half the total time and $v_2$ for the remaining half, then: $$v_{av} = \frac{v_1 + v_2}{2}$$
2. Distance-Averaged Speed
If a particle covers different distances $d_1, d_2, d_3, \dots$ with speeds $v_1, v_2, v_3, \dots$, then:
$$v_{av} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}$$
$$v_{av} = \frac{d_1 + d_2 + d_3 + \dots}{t_1 + t_2 + t_3 + \dots}$$
$$v_{av} = \frac{d_1 + d_2 + d_3 + \dots}{\frac{d_1}{v_1} + \frac{d_2}{v_2} + \frac{d_3}{v_3} + \dots}$$
Special Cases:
- If a particle moves half the total distance at $v_1$ and the other half at $v_2$, then:
$$v_{av} = \frac{2 v_1 v_2}{v_1 + v_2} $$
- If a particle moves one-third of the distance at $v_1$, the next one-third at $v_2$, and the last one-third at $v_3$, then:
$$v_{av} = \frac{3 v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1} $$
FAQs
Q1: Is average speed a vector or a scalar?
A: Average speed is a scalar quantity because it depends only on the magnitude of the total distance traveled, not on direction.
Q2: Why is average speed always greater than or equal to average velocity?
A: Since displacement is always ≤ distance, and velocity is based on displacement, the magnitude of average velocity is always ≤ average speed.
Multiple Choice Questions (MCQs) with Answers and Explanations
Q1: A car travels 100 m in 5 seconds and then 150 m in 10 seconds. What is its average speed?
(a) 10 m/s
(b) 12 m/s
(c) 15 m/s
(d) 17 m/s
Answer: (b) 12 m/s
Explanation: $$v_{av} = \frac{\text{Total Distance}}{\text{Total Time}}$$
$$v_{av} = \frac{100 + 150}{5 + 10} = \frac{250}{15} = 12 \text{ m/s}$$
Q2: A bus moves at 40 km/h for 2 hours and then at 60 km/h for 3 hours. What is its average speed?
(a) 48 km/h
(b) 50 km/h
(c) 52 km/h
(d) 54 km/h
Answer: (c) 52 km/h
Explanation:
Total distance traveled: (40×2)+(60×3)=80+180=260 km
Total time taken: 2+3=5 hours
Average speed:
$$v_{av} = \frac{\text{Total Distance}}{\text{Total Time}}$$
$$v_{av} = \frac{260}{5} = 52 \text{ km/h}$$
Q3: A train moves half the total distance at 30 km/h and the other half at 60 km/h. What is its average speed?
(a) 40 km/h
(b) 42 km/h
(c) 45 km/h
(d) 48 km/h
Answer: (a) 40 km/h
Explanation: Using the distance-averaged speed formula:
$$v_{av} = \frac{2 v_1 v_2}{v_1 + v_2} $$
$$v_{av}= \frac{2 \times 30 \times 60}{30 + 60}$$
$$v_{av} = \frac{3600}{90} = 40 \text{ km/h}$$
Q4: A cyclist covers one-third of the total distance at 20 km/h, next one-third at 30 km/h, and the last one-third at 60 km/h. What is the average speed?
(a) 30 km/h
(b) 32 km/h
(c) 35 km/h
(d) 40 km/h
Answer: (b) 32 km/h
Explanation:
Using the formula for three equal distances:
$$v_{av} = \frac{3 v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1}$$
$$v_{av} = \frac{3 \times 20 \times 30 \times 60}{(20 \times 30) + (30 \times 60) + (60 \times 20)}$$
$$v_{av} = \frac{108000}{3360} = 32.14 \approx 32 \text{ km/h}$$
Q5: A person walks 2 km at 5 km/h, then jogs 3 km at 10 km/h. What is the average speed?
(a) 6 km/h
(b) 6.5 km/h
(c) 7 km/h
(d) 7.5 km/h
Answer: (c) 7 km/h
Explanation:
Total distance traveled: 2+3=5 km
Time taken for first part: $$t_1=\frac{2}{5} = 0.4 \text{ hours}$$
Time taken for second part: $$t_2=\frac{3}{10} = 0.3 \text{ hours}$$
Total time taken: 0.4+0.3=0.7 hours
Average speed:
$$v_{av} = \frac{\text{Total Distance}}{\text{Total Time}}$$
$$v_{av} = \frac{5}{0.7} = 7.14 \approx 7 \text{ km/h}$$
Q6: A car travels 100 m in 5 seconds and then 150 m in 10 seconds. What is its average speed?
(a) 10 m/s
(b) 12 m/s
(c) 15 m/s
(d) 17 m/s
Answer: (b) 12 m/s
Explanation: Average speed:
$$v_{av} = \frac{\text{Total Distance}}{\text{Total Time}}$$
$$v_{av} = \frac{(100 + 150)}{(5 + 10)} = \frac{250}{15} = 12 \text{ m/s}$$
These MCQs help in understanding how to calculate average speed under different conditions, which is crucial for JEE, NEET, and CBSE Board Class 11 exams.
Conceptual Questions with Answers
Q1: Can average speed be zero?
A: No, unless the total distance traveled is zero. However, average velocity can be zero if the initial and final positions are the same.
Do You Know?
- Average speed and velocity are the same only for straight-line motion without turning back.
- If a body moves at a constant speed in a circular path, its average velocity over one complete revolution is zero.
Worksheet
Solve the following problems:
- A train covers half its journey at 40 km/h and the other half at 60 km/h. Find its average speed.
- A cyclist moves 100 m in 10 sec and then 150 m in 15 sec. Find the average speed.
Test Paper (Total Marks: 10)
- Define average speed. (2 marks)
- A car moves at 30 km/h for 2 hours and then at 50 km/h for 3 hours. Find its average speed. (4 marks)
- Derive the formula for distance-averaged speed when a particle moves equal distances at different speeds. (4 marks)
Important Points for Quick Revision
- $v_{av} = \frac{\text{Total Distance}}{\text{Total Time}}$
- Time-averaged speed considers time intervals; distance-averaged speed considers distances.
- Use harmonic mean formula for distance-averaged speed when distances are equal.
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