a cyclist completes a lap around a circular track at a speed of 10m/s in 40s what is the displacement of the cyclist
ZERO !!!
DISTANCE is how far you go
In this case 2 pi R
HOWEVER
Displacement is the vector from where you start to where you are.
In this case he went all the way around, ending up where he started, so his DISPLACEMENT is ZERO
That is really, really important.
To find the displacement of the cyclist, we need to determine the distance traveled and the direction. Since the cyclist completes a lap around a circular track, the total distance traveled is equal to the circumference of the circle.
To calculate the circumference of the circular track, we can use the formula:
C = 2πr
However, we do not have the radius (r) of the circular track. Since we are given the speed (v) of the cyclist, and we can assume the cyclist maintained a constant speed throughout the lap, we can find the radius using the formula for linear velocity (v) and angular velocity (ω):
v = ωr
Rearranging the formula, we have:
r = v / ω
The time it takes to complete one lap around the circular track is 40 seconds, so the angular velocity (ω) is equal to:
ω = 2π / t
Plugging in the given values:
ω = 2π / 40
Now, let's calculate the radius (r):
r = v / ω = 10 / (2π / 40)
Simplifying the equation, we get:
r = 400 / π
Now that we have the radius of the circular track, we can calculate the circumference (C):
C = 2πr = 2π * (400 / π) = 800 meters
Therefore, the displacement of the cyclist is equal to the circumference of the track, which is 800 meters.