A car races on a circular track of radius r.
(a) Write an equation for the car's average speed when it travels a complete lap in time t.
(b) The radius of the track is 100 m and the time to complete a lap is 14 s. Show that the average speed around the track is 45 m/s.
a. Circumference = pi*2r = 3.14*2r =
6.28r
V = C/t = 2pi*r/t
b. V = 6.28*100m/14s = 45 m/s.
(a) Well, the car travels a distance equal to the circumference of the circular track, which is given by C = 2πr. And since speed is distance over time, the average speed of the car would be:
average speed = total distance / total time
For a complete lap, the total distance is equal to the circumference C, so the average speed would be:
average speed = C / t
Plugging in the value for the circumference, we get:
average speed = 2πr / t
(b) Now let's calculate the average speed for the given values. The radius of the track is 100 m and the time to complete a lap is 14 s. Substituting these values into our equation:
average speed = 2π(100) / 14
Calculating this, we get:
average speed ≈ 6.28 * 100 / 14
average speed ≈ 628 / 14
average speed ≈ 44.857 m/s
So, the average speed around the track is approximately 44.857 m/s, which we can round up to 45 m/s.
(a) The average speed of the car can be calculated by dividing the total distance traveled by the total time taken. In this case, the car travels a complete lap, which is equivalent to the circumference of the circular track.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.
So, the distance traveled by the car in one lap is 2πr. Dividing this by the time taken (t), we get the average speed of the car, which can be expressed as:
Average Speed = (2πr) / t
(b) Given that the radius of the track is 100 m and the time to complete a lap is 14 s, we can substitute these values into the formula derived in part (a):
Average Speed = (2π * 100) / 14
Calculating this expression:
Average Speed = (200π) / 14
Approximating the value of π to 3.1416:
Average Speed ≈ (200 * 3.1416) / 14
Average Speed ≈ 628.32 / 14
Average Speed ≈ 44.88 m/s
Therefore, the average speed around the track is approximately 44.88 m/s, which can be rounded to 45 m/s.
(a) The average speed of an object is defined as the total distance traveled divided by the time taken. In this case, the car travels a complete lap on a circular track, which is equivalent to the circumference of the circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
So, the distance traveled by the car during a complete lap is C = 2πr.
Therefore, the equation for the car's average speed when it travels a complete lap in time t is:
average speed = total distance traveled / time taken = (2πr) / t.
(b) Given that the radius of the track (r) is 100 m and the time to complete a lap (t) is 14 s, we can substitute these values into the equation for average speed:
average speed = (2π * 100) / 14 = 628.32 / 14 ≈ 44.88 m/s.
Hence, the average speed around the track is approximately 44.88 m/s, which can be rounded to 45 m/s.