the velocity time graph relation of an electron starting from rest is given by v=kt where k=2m per second square.the distance trasveresed in 3 sec. is

To find the distance traversed by the electron in 3 seconds, we can use the relationship given by the velocity-time graph and the formulas of motion. In this scenario, the velocity \( v \) of the electron is described by the equation \( v = kt \), where \( k = 2 \, \text{m/s}^2 \). This means that the velocity increases linearly over time because the electron starts from rest.

Understanding Velocity and Distance

The formula for velocity tells us how fast the electron is moving at any point in time. Since the electron starts from rest, its initial velocity when \( t = 0 \) is 0 m/s. As time progresses, the velocity increases due to the constant acceleration defined by \( k \).

Calculating Velocity at Specific Time

First, we can calculate the velocity of the electron at \( t = 3 \, \text{s} \):

• Using the formula \( v = kt \), we substitute \( k = 2 \, \text{m/s}^2 \) and \( t = 3 \, \text{s} \):
• So, \( v = 2 \cdot 3 = 6 \, \text{m/s} \).

Finding the Distance Traveled

To find the distance traversed, we can use the formula for distance when the acceleration is constant:

• The formula is \( d = ut + \frac{1}{2} a t^2 \), where:
• \( d \) is the distance traveled,
• \( u \) is the initial velocity (0 m/s in this case),
• \( a \) is the acceleration (which is equal to \( k \), or \( 2 \, \text{m/s}^2 \)),
• \( t \) is the time (3 seconds).

Substituting these values into the formula:

• Since \( u = 0 \, \text{m/s} \):
• \( d = 0 \cdot 3 + \frac{1}{2} \cdot 2 \cdot (3)^2 \)
• \( d = 0 + \frac{1}{2} \cdot 2 \cdot 9 \)
• \( d = 9 \, \text{m} \).

Conclusion

Therefore, the distance traversed by the electron in 3 seconds is 9 meters. This result illustrates how the distance increases as a function of time when an object accelerates from rest under constant acceleration. If you visualize this on a velocity-time graph, the area under the curve represents the distance traveled, which in this case is a triangle formed by the line depicting velocity over time.