Question

What does the speedometer measure kept in motorbike? (A) Average Velocity (B) Average speed (C) instantaneous speed (D) instantaneous Velocity

Short answer

(C) Instantaneous Speed

Step-by-step solution

Understand the definitions

To find the most accurate answer, we first need to understand the key differences between the terms given in the options: 1. Average Velocity: The distance covered in a particular direction divided by the time taken. 2. Average Speed: The total distance traveled divided by the time taken, irrespective of the direction. 3. Instantaneous Speed: The speed of an object at a specific point in time. 4. Instantaneous Velocity: The velocity of an object at a specific point in time, including both the speed and direction.

Identify the purpose of a speedometer

A speedometer in a motorbike is designed to display the current (instantaneous) speed of the motorbike for the rider. It does not provide information about the direction of travel, nor does it measure average speed or velocity over a period of time.

Choose the correct answer

Based on the understanding of the purpose of a speedometer, we can choose the appropriate answer: (C) Instantaneous Speed The speedometer measures the instantaneous speed of the motorbike.

Key concepts

Speedometer

A speedometer is an essential instrument on any vehicle, including motorbikes, and it plays a crucial role in road safety. Mounted on the dashboard, a speedometer shows the driver how fast they are moving at any particular moment. This is what is known as the **instantaneous speed**.

• The speedometer helps ensure that the driver maintains a safe and legal speed.
• While driving, it displays the speed immediately without any delay.
• It does not show the direction, only how fast the vehicle is going.

By focusing only on the current speed, speedometers allow drivers to adjust their speed quickly if needed, ensuring they comply with local speed limits and maintain safe driving practices.

Average Velocity

Average velocity is a measure that includes both the magnitude and direction of travel over a specified duration. It represents the total displacement divided by the total time taken.

• Displacement refers to the change in position in a specific direction.
• The formula for average velocity is \( v_{avg} = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is displacement, and \( \Delta t \) is the time taken.
• Unlike speed, average velocity can be negative, indicating movement in the opposite direction.

Understanding average velocity is essential in fields such as physics and engineering where both the speed and direction of an object is important, unlike what a speedometer provides.

Instantaneous Velocity

Instantaneous velocity is a concept that provides more depth than just instantaneous speed, as it includes both the magnitude and direction at any given point in time.

• Instantaneous velocity can be thought of as the velocity of an object at a particular instant.
• The formula is expressed as \( v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} \), representing the derivative of position with respect to time.
• Instantaneous velocity provides a comprehensive understanding of the movement as it incorporates both current speed and direction.

While speedometers measure instantaneous speed, instruments such as GPS can better assist in providing instantaneous velocity.

Average Speed

Average speed is a simpler concept compared to velocity because it only considers how much total ground has been covered over a period of time, disregarding direction.

• The formula for average speed is \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \).
• It is always a positive value, reflecting the total path length divided by time.
• Average speed does not provide any information about specific speeds or directions along the journey.

This measurement is helpful for determining how efficient a travel route was, but it does not give the specific details seen in instantaneous measurements. Average speed is generally not what a speedometer measures, as instantaneous data is more critical for real-time driving decisions.