a body covers a circular path of radius 'R' in 20 seconds.calculate the distance and displacement of the body at the end of 70 seconds.
To calculate the distance covered by the body at the end of 70 seconds, we need to first find the total number of complete circular paths the body covers within that time.
Given that the body covers a circular path of radius 'R' in 20 seconds, we can calculate the time taken to complete one full circle as follows:
Time for one full circle = 20 seconds
Time for 70 seconds = 70 seconds
Now, let's calculate the number of complete circles covered in 70 seconds:
Number of complete circles = Time for 70 seconds / Time for one full circle = 70 seconds / 20 seconds = 3.5 circles
Since the body covers a complete circle in 20 seconds, it means that after 70 seconds, the body finishes 3 complete circles and reaches halfway through the fourth circle.
Now, let's calculate the distance covered by the body:
Distance covered by the body = Circumference of a circle × Number of complete circles
Circumference of a circle = 2πR (where R is the radius)
Number of complete circles = 3 (as calculated earlier)
Distance covered by the body = 2πR × 3 = 6πR
Therefore, the distance covered by the body at the end of 70 seconds is 6πR.
Now, let's calculate the displacement of the body. Displacement is the shortest straight-line distance between the initial and final positions of the body.
The body begins and ends on the same circle, so the displacement will be the distance between the starting point and the ending point of the fourth circle.
To find the displacement, we need to find the arc length covered by the body in the fourth circle.
Arc length = circumference of a circle × (angle subtended at the center / 360 degrees)
The angle subtended at the center by the fourth circle is (1/2) × 360 degrees = 180 degrees.
Arc length = 2πR × (180/360) = πR
Therefore, the displacement of the body at the end of 70 seconds is πR.
it has gone 3.5 laps, each of length 2πR
its displacement is just one diameter away from where it started.