Ana run in a circular path. The dimension of the circular path is r = 10m , she finished it in 20 seconds. Find his speed, distance, displacement and velocity.
10m east (starting point) and 10 m south (finish point)
Circumference=pi*2r = 3.14 * 20=62.83 m.
d = (270o/360o) * 62.83m = 47.12 m. =
Distance traveled.
d = r*t = 47.12 m.
r = 47.12/t = 47.12/20 = 2.36 m/s=Speed.
Displacement = 10m[270] - 10[0o]
-10 - 10i = -14.14m.[45o] = 14.14m[-45o]
To find Ana's speed, we need to divide the distance she traveled by the time it took for her to complete the circular path.
Speed = Distance / Time
Distance = 2πr (circumference of a circle)
Time = 20 seconds
Given that the radius r is 10m, we can substitute the values into the formula:
Distance = 2π(10) = 20π meters
Now we can calculate the speed:
Speed = Distance / Time = (20π meters) / (20 seconds)
To simplify the speed, we divide both the numerator and denominator by 20:
Speed = π meter/second
So Ana's speed is π meter/second.
To calculate the distance, we use the formula for the circumference of a circle:
Distance = 2πr = 2π(10) = 20π meters
So the distance Ana covered is 20π meters.
To find the displacement, we need to determine the straight-line distance and direction from the starting point to the finishing point.
Using the given information, we know Ana traveled 10 meters east at the starting point and 10 meters south at the finish point. Drawing a diagram, we can see that the displacement is the straight-line distance between the starting and ending points, which is the hypotenuse of a right-angled triangle with sides of 10 meters each.
Using the Pythagorean theorem, we can calculate the displacement:
Displacement = √(10^2 + 10^2) = √(100 + 100) = √200 meters
So the displacement is approximately 14.14 meters.
Lastly, velocity is a vector quantity that includes both speed and direction. Since Ana traveled in a circular path, her direction is constantly changing. Therefore, we cannot calculate the velocity without additional information, such as the direction at different points along the path.