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Chapter 2: Problem 33

When can the speed and average speed of a vehicle be equal?

Short Answer

Expert verified
Answer: The speed and average speed of a vehicle will be equal when the vehicle travels at a constant speed without any abrupt change in its acceleration.

Step by step solution

01

Understanding Speed

Speed is the measure of how fast an object is moving. It is defined as the distance covered divided by the time taken to cover that distance, typically measured in units such as meters per second (m/s) or kilometers per hour (km/h). Mathematically, speed is given by the formula \(speed = \frac{distance}{time}\).
02

Understanding Average Speed

Average speed is the measure of the total distance covered divided by the total time taken. It is obtained by dividing the total distance covered by the total time taken during the entire journey. Mathematically, average speed is given by the formula \(average \ speed = \frac{total \ distance}{total \ time}\).
03

Comparing Speed and Average Speed

Speed represents the instantaneous value of how fast an object is moving at any given moment, while average speed represents a summary of the overall journey. In order to compare the two, we need to consider the impact of acceleration (changes in speed) and when acceleration is constant.
04

Identifying Conditions when Speed and Average Speed are Equal

The condition where speed and average speed of a vehicle will be equal is when the acceleration is constant and there are no abrupt changes in speed during the journey (i.e., no sudden stops or rapid accelerations). In this case, the instantaneous speed remains the same throughout the journey and is equal to the average speed. Formally, this condition can be written as \(speed = \frac{distance}{time} = \frac{total \ distance}{total \ time}\). In conclusion, the speed and average speed of a vehicle can be equal when the vehicle travels at a constant speed without any abrupt change in its acceleration.

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Most popular questions from this chapter

Define amplitude and frequency. Write their SI units.

Name the physical quantity that measures fastness or slowness of a moving object.

A body moves with uniform speed of \(\mathrm{u} \mathrm{m} \mathrm{s}^{-1}\) towards east, then the body is said to possess _ velocity.

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Choose the correct statement (s). (1) Speed and velocity both have same units. (2) If a body has a speed of \(50 \mathrm{~m} \mathrm{~s}^{-1}\) in a straight line path, then its velocity is \(180 \mathrm{~km} \mathrm{~h}^{-1}\) (3) Speed of a vehicle is measured by a device called speedometer. (4) All the above
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