The instantaneous velocity of a body can be measured

Options

A. Graphically
B. Vectorially
C. By speedometer
D. None of these

Answer

To solve the question regarding how to measure the instantaneous velocity of a body, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Instantaneous Velocity**:
Instantaneous velocity is defined as the velocity of an object at a specific moment in time. It can be thought of as the limit of the average velocity as the time interval approaches zero.

2. **Using a Speedometer**:
One of the most common ways to measure instantaneous velocity is by using a speedometer in a vehicle. The speedometer provides a direct reading of the speed at any given moment.

3. **Using a Stopwatch and Measuring Distance**:
Another method involves measuring the distance traveled by the body over a very short time interval.
- Start a stopwatch when the body passes a certain point.
- Stop the stopwatch when the body has traveled a small, measurable distance.
- Calculate the instantaneous velocity using the formula:
\[ v = \frac{d}{t} \]
where \( v \) is the instantaneous velocity, \( d \) is the distance traveled, and \( t \) is the time taken.

4. **Graphical Method**:
If you have a position-time graph of the body’s motion, you can determine the instantaneous velocity by finding the slope of the tangent line at the point of interest on the curve.
- Draw a tangent line at the point on the graph.
- Calculate the slope of this tangent line, which represents the instantaneous velocity.

5. **Using Calculus**:
For more advanced methods, if the position of the body as a function of time is known (e.g., \( s(t) \)), the instantaneous velocity can be calculated by taking the derivative of the position function with respect to time:
\[ v(t) = \frac{ds}{dt} \]
This gives the instantaneous velocity at any point in time.