a bird flies for 4 second with a velocity of |t-2| m/s . in a straight line . it covers a distance of

Question

Answer

Explanation of a Bird's Flight with Changing Velocity

Description of the Scenario

A bird is flying for 4 seconds in a straight line with a velocity that changes over time. The velocity is given by the absolute value of t-2, where t is the time elapsed in seconds. The task is to determine the distance covered by the bird during this time period.

Calculation of the Distance Covered

To calculate the distance covered by the bird, we need to integrate the velocity function over the time period of 4 seconds. The velocity function can be broken down into two parts:

When t is less than 2, the velocity function is given by 2-t.

When t is greater than or equal to 2, the velocity function is given by t-2.

We can integrate each part separately to get the total distance covered by the bird:

For t less than 2: The integral of 2-t over the time period of 0 to 2 is equal to 2. This means that the bird travels a distance of 2 meters during the first 2 seconds of its flight.

For t greater than or equal to 2: The integral of t-2 over the time period of 2 to 4 is equal to 0. This means that the bird does not travel any distance during the last 2 seconds of its flight.

Therefore, the total distance covered by the bird is 2 meters.

Answer

In a straight line distance =displacement.
we know velocity =displacement/time
here t=4s
v=4-2=2m/s
v=s/t
2=s/4
s=8 metres

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