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Chapter 3: Problem 19

The average speed \(=\) uniform speed \(=10 \mathrm{~km} \mathrm{~h}^{-1}\)

Short Answer

Expert verified
Answer: In this exercise, the average speed or uniform speed is 10 km/h. It can be used in practical applications to determine the distance covered or time taken when adequate information is provided.

Step by step solution

01

Understand average or uniform speed

The average speed or uniform speed is defined as the total distance covered divided by the total time taken. In simple words, it is the speed maintained consistently throughout a journey.
02

Identify the given information

In this exercise, we are given the average speed or uniform speed which is equal to 10 km/h.
03

Use the average speed formula

The formula for average speed can be written as: \(\mathrm{Average\: Speed} = \frac{\mathrm{Total\: Distance}}{\mathrm{Total\: Time}}\)
04

Apply the given information to the formula

In this case, we know the average speed, and it is equal to 10 km/h. If we need to find the distance covered or time taken, we need further information. Otherwise, we can only use the given average speed in various practical applications.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Uniform Speed
Uniform speed means an object is moving at a constant speed throughout the entire journey. Imagine you're on a road trip and your car's speedometer stays fixed at 60 km/h. You're driving at uniform speed if the car's speed doesn't vary - no faster, no slower.
This is similar to the average speed when the speed doesn't fluctuate over time. For any trip where the speed is constant, the average speed is simply the same as the uniform speed. It's a straightforward concept but very crucial in understanding speed in kinematics.
Knowing uniform speed helps simplify problems by allowing the use of basic formulas, reducing complex movements to constant motion.
  • Useful for problem-solving in physics and everyday scenarios.
  • Makes it easier to predict travel times and distances.
Distance-Time Relationship
The relationship between distance and time is fundamental to understanding motion. In simple terms, if you know how fast you're going (speed) and how long you're traveling (time), you can figure out how far you've gone (distance). This relationship is captured by a formula:
\[\mathrm{Distance} = \mathrm{Speed} \times \mathrm{Time}\]
Understanding this relationship helps us solve problems where we need to find out one of these three variables when the other two are known.
  • It's a linear relationship: doubling the time at constant speed doubles the distance.
  • Knowing any two of the three variables (speed, time, distance) helps to find out the third one.
This makes it possible to plan journeys, calculate expected arrival times, or even decide the best routes to take based on speed limits.
Speed Calculation
Calculating speed is one of the first steps to understanding movement. Speed tells us how much distance an object covers over a certain period of time. Using the formula:
\[\mathrm{Speed} = \frac{\mathrm{Distance}}{\mathrm{Time}} \]
We can determine how fast something is moving if we know how far it goes and how long it takes.
Calculating speed is crucial in many areas:
  • Helps in determining travel time for various modes of transport.
  • Essential for safety calculations, such as stopping distances for vehicles.
  • Important in sports to track performance improvements.
Kinematics
Kinematics is the branch of physics that deals with the motion of objects without considering the forces causing the motion. It centers on three key variables: displacement, velocity, and acceleration.

Kinematics allows us to describe motion using formulas and diagrams, offering insights into how objects move at different speeds and directions. For example, understanding kinematics can help predict how far a car will travel in a given time if it accelerates or maintains constant speed.
  • Provides a framework for understanding complex motion scenarios.
  • Utilizes time-distance graphs to illustrate the motion.
  • Helps in designing systems and simplifying real-world motion problems.
By mastering the principles of kinematics, students can better solve physics problems and apply these concepts to practical situations.

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Most popular questions from this chapter

Motion along a straight line. (a) The motion of coin on a carrom board. (b) The motion of air bus in straight line. Circular motion \(\quad\) (a) Earth revolving around the sun. (b) Potter's wheel. Periodic motion \(\quad\) (a) The swinging pendulum of a wall clock. (b) Halley commet visits earth at regular periods.

The maximum displacement of the vibrating particle is called amplitude. S.I unit is \(\mathrm{m}\). The number of vibrations per second is frequency. SI unit is hertz (Hz).

Fill in the Blanks. \(\frac{1}{1000}\) 1000 millisecond \(=1 \mathrm{~s}\) \(\Rightarrow 1\) millisecond \(=\frac{1}{1000}\) th part of a second.

Consider a body moving with initial velocity u. Let its velocity change to \(\mathrm{v}\), in time ' \(\mathrm{t}^{\prime}\). Then, the change in velocity is \(=\mathrm{v}-\mathrm{u}\). The change in velocity per unit time \(=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) By definition, the change in velocity per unit time is acceleration, a. Thus, \(\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) or \(\mathrm{v}-\mathrm{u}=\) at \(\mathrm{v}=\mathrm{u}+\mathrm{at}\)

Take the bob of the pendulum to one side so that the pendulum makes \(5^{\circ}\) with the vertical and release the bob. Start the stop watch when the bob is at the mean or extreme position and find the time taken by the pendulum to complete 20 oscillations. Dividing the time for 20 oscillations by 20 gives the time period (T) of the pendulum. The above experiment can be repeated for different lengths \((80 \mathrm{~cm}\),
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