A particle moves in a circle of radius 21 22m with constant speed 1m/s. find magnitude of average velocity
Answers
Average velocity of a Body is defined as the vectorial Change in Position (displacement) over a given time.
here the Body is moving in a circular path of radius 21/22 => the circumference of the circle is 2*pi*r = 2*(22/7)*(21/22)=6.
therefore the Body takes 6 seconds to travel the whole circular path. Now in 2 seconds, it will travel to a Point on the circle which makes an angle 120 degrees with the Initial Position about the centre.
Therefore the displacement of the Body is = the distance between Initial and final Points. It can be calculated (using some trignometry) as r*sqrt(3) = 21/22 * sqrt(3).
and the time is 2 sec => the average velocity = sqrt(3) * (21/22)/2
And the average acceleration is defined as the vectorial difference between final and Initial velocities over time. The vectorial difference in this case gives the Magnitude as 1 and the time is 2 sec, meaning the average acceleration = 0.5
An average value of a quantity is defined as the difference of Initial and final values of it's time differential over time. In case of velocity it is the difference of Position (time differential of velocity) over time. Similarly, for acceleration, it is difference in velocity over time. And in this case the quantities are vectors, so it would be vectorial difference.