Find the time t from the X-ray graph of a particle such that the average velocity of the particle during the period 0 to t is zero

To determine the time \( t \) from the X-ray graph of a particle where the average velocity from time \( 0 \) to \( t \) is zero, we need to understand a few key concepts about average velocity and the graphical representation of motion.

Understanding Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. Mathematically, it can be expressed as:

Average Velocity = (Displacement) / (Time)

Displacement and Its Importance

Displacement is the difference between the final position and the initial position of the particle. For the average velocity to be zero, the displacement must also be zero. This means that the particle must return to its starting point by time \( t \).

Analyzing the X-ray Graph

When looking at the X-ray graph, you will typically see a plot of position versus time. To find the time \( t \) where the average velocity is zero, follow these steps:

• Identify the Initial Position: Look for the position of the particle at time \( t = 0 \).
• Track the Motion: Observe how the position changes over time. Note where the particle moves away from the starting point and where it returns.
• Find the Return Point: The time \( t \) you are looking for is when the particle returns to its initial position.

Example Scenario

Imagine a particle that moves in a straight line. At \( t = 0 \), it starts at position \( 0 \). It moves to position \( 5 \) at \( t = 2 \) seconds, then returns to position \( 0 \) at \( t = 4 \) seconds. In this case:

• Initial position at \( t = 0 \) is \( 0 \).
• Final position at \( t = 4 \) is also \( 0 \).

Thus, the average velocity from \( 0 \) to \( 4 \) seconds is:

Average Velocity = (0 - 0) / (4 - 0) = 0

Finding the Specific Time

To find the specific time \( t \) where the average velocity is zero, you would look for the point on the graph where the position returns to the initial value. If the graph shows multiple oscillations, you may find several times \( t \) where this condition holds true.

In summary, to find the time \( t \) where the average velocity is zero, identify when the particle's position returns to its starting point. This will give you the required time interval where the average velocity equals zero.