A body travels along a circular path of radius 70 m.After travelling half a revolution in 20 s find the ;
1.average velocity
2.average speed
To find the average velocity and average speed, we need to determine the distance traveled by the body during half a revolution.
1. Distance traveled during half a revolution:
The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle.
In this case, the radius is 70 m, so the circumference is: C = 2 * π * 70 = 140π m.
Since the body traveled half a revolution, the distance covered is half the circumference, which is: (1/2) * 140π = 70π m.
2. Average velocity:
The average velocity is defined as the displacement over the total time. Since the body traveled in a circular path, it returned back to the starting point, which means the displacement is zero.
Therefore, average velocity = displacement / time = 0 / 20 = 0 m/s.
3. Average speed:
The average speed is defined as the total distance traveled over the total time.
Average speed = total distance / total time = (70π m) / 20 s ≈ 11.09 m/s.
So, the answers are:
1. Average velocity = 0 m/s.
2. Average speed ≈ 11.09 m/s.
To find the average velocity and average speed of a body traveling along a circular path, we need to first understand the definitions of these terms.
1. Average velocity: It is the displacement of an object divided by the time interval during which the displacement occurred. The displacement is the change in position of an object, which is a vector quantity. Average velocity is also a vector quantity and is given by the formula:
Average velocity = Displacement / Time interval
2. Average speed: It is the total distance traveled by an object divided by the time taken. Unlike average velocity, average speed is a scalar quantity as it does not take into account the direction of motion. Average speed is given by the formula:
Average speed = Total distance traveled / Time taken
Now, let's calculate the average velocity and average speed using the given information.
Given:
Radius of the circular path (r) = 70 m
Time taken to travel half a revolution (t) = 20 s
To find the displacement, we need to calculate the distance traveled along the half-revolution of the circular path. The distance along a circle is given by the formula:
Distance = Circumference of the circle * Fraction of the revolution
For half a revolution, the fraction of the revolution is 1/2.
Circumference of a circle = 2 * π * r
= 2 * π * 70 m
= 140π m
Distance along half a revolution = (140π m) * (1/2)
= 70π m
Now, let's calculate the average velocity:
Average velocity = Displacement / Time interval
The displacement is the same as the distance traveled along half a revolution, which is 70π m.
Average velocity = (70π m) / (20 s)
= 3.5π m/s
So, the average velocity is 3.5π m/s.
Next, let's calculate the average speed:
Average speed = Total distance traveled / Time taken
The total distance traveled is the same as the distance traveled along half a revolution, which is 70π m.
Average speed = (70π m) / (20 s)
= 3.5π m/s
So, the average speed is also 3.5π m/s.
It's wrong
The body changed position, from one side of the circle, to the other.
displacement=changeposition/time=2PIr/20
there has to be a direction associated with displacement, my drawing has it West.
average speed: distance/time=2PIr/20
average velocity: 2PIr/20 West