A particle travels 15 times around a 10-cm radius circle in 42 seconds. What is the average speed (in m/s) of the particle?
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I think I use the
v=(2pi*r)/T
equation? Right?
Not quite. Since it goes around 15 times in 42 seconds, you need to multiply (2pi*r)/T by 15 if T = 42 s.
Yes, you are correct. The equation you mentioned, v = (2πr)/T, can be used to calculate the average speed of the particle.
Where:
v = average speed
r = radius of the circle
T = time taken to complete the motion
In this case, the radius is given as 10 cm (0.1 m) and the time taken is 42 seconds.
Substituting the values into the equation, we can calculate the average speed:
v = (2π * 0.1) / 42
Now we can solve the equation to find the average speed.
Yes, you are correct. To find the average speed of the particle, you can use the formula:
v = (2πr) / T
where:
v = average speed of the particle
r = radius of the circle
T = total time taken to complete the circle
In this case, the radius of the circle is given as 10 cm, which can be converted to meters by dividing by 100:
r = 10 cm / 100 = 0.1 m
The total time taken to complete 15 circles is given as 42 seconds, so the time taken to complete one circle (T) would be:
T = 42 seconds / 15 = 2.8 seconds
Now, we can substitute the values into the formula to find the average speed:
v = (2π * 0.1) / 2.8
Calculating this, we get:
v ≈ 0.226 m/s
Therefore, the average speed of the particle is approximately 0.226 m/s.