Question

radius vector of particle moving on a circle is given by r vector = 2cos2ti^ + 2sin2tj^ the speed of the particle is ( where ris in m and t is in s)​

Answer 1

Answer:

4cos4ti^.

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Answer 2

Answer:

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A particle is moving in a circle of radius R with constant speed. The time period of particle is T=1 second. In a time t= T/6, if the difference between the average speed and magnitude of average velocity is 2m/s, find the radius of circle.

Explanation:

radius vector of particle moving on a circle is given by r vector = 2cos2ti^ + 2sin2tj^ the speed of the particle is ( where ris in m and t is in s)Since the time period is 1 sec , average speed will be = 2×3.14×r = 6.28r

Now, let the particle start from the top of the circle with velocity In horizontal direction,

Considering X axis along horizontal direction

The initial position vector of particle= r(j)

After 1/6 sec particle has covered 60 degrees,

Final position vector of particle= rcos60(j)+rsin60(i) 

Change in position = (rcos60-r)(j) + rsin60(i)

Average velocity = change in position/time = 6(rcos60-r)(j) + 6rsin60(i).

This will have a magnitude of  6r

now A/Q, 6.28r-6r =2

r=7.062 m I HOPE IT WILL HELP YOU AND THIS INFORMATION IS USED TO U OKAY BYE