Instantaneous velocity and instantaneous speed

The video tutorial explains the difference between average and instantaneous velocity using the example of a train journey. It highlights that average velocity provides information over a time interval, while instantaneous velocity gives the speed at a specific moment. The concept of instantaneous velocity is defined mathematically as the derivative of displacement with respect to time. The tutorial also demonstrates how to calculate instantaneous velocity graphically by finding the slope of the tangent to the position-time curve at a given point.

What does average velocity fail to provide?

• The direction of motion

• The total time taken

• The speed at a specific moment

• The total distance traveled

How is instantaneous velocity defined mathematically?

• As the limit of average velocity over a small time interval

• As the sum of all velocities

• As the integral of acceleration

• As the product of speed and time

What does the derivative of displacement with respect to time represent?

• Average speed

• Instantaneous velocity

• Total distance

• Acceleration

How can instantaneous velocity be determined graphically?

• By counting the number of peaks in the graph

• By finding the area under the curve

• By measuring the distance between two points

• By calculating the slope of the tangent to the position-time curve

In the train example, what is needed to find the instantaneous velocity at a specific time?

• The distance covered

• The slope of the tangent at that time

• The total travel time

• The average speed