A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car?

Question

A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car?

Answer 1

v^2/R

where v = 2 pi R /50 = 60
so
R = 3000/(2 pi) = 1500/pi

Ac = 60^2 (pi/1500)

Answer 2

Well, if the race car is moving with a constant speed, then there is no change in velocity, which means the acceleration is zero. It's like me trying to get out of bed in the morning – my acceleration is pretty much nonexistent!

Answer 3

To find the magnitude of acceleration of the race car, we need to first understand that acceleration is the rate at which the velocity of an object changes. In this case, as the race car moves in a circular track, its velocity is constantly changing direction, even if its speed remains constant.

The formula to find the acceleration of an object moving in a circular path is given by:

a = (v^2) / r

Where:
a = acceleration
v = velocity
r = radius of the circular path

We are given the speed of the race car, which is 60 m/s, but we need to convert it into velocity. Velocity is a vector quantity and includes both magnitude and direction. Since the race car moves in a circular path, its velocity is constantly changing direction but always tangent to the circle.

To find the velocity, we need to determine the circumference of the circular track using the formula:

C = 2πr

Where:
C = circumference
π = pi (approximately 3.14159)
r = radius of the circular track

We know that the race car completes one lap around the circular track in 50 s. Since the velocity is the distance traveled divided by the time taken, we can find the circumference using the formula:

C = s / t

Where:
C = circumference
s = distance traveled (circumference of the circular track)
t = time taken (50 s)

Rearranging the formula, we have:

C = v * t

Substituting the given values, we get:

C = 60 m/s * 50 s

Now, we can use the equation for circumference to solve for the radius (r):

2πr = C

Rearranging the formula, we have:

r = C / (2π)

Substituting the value of C, we get:

r = (60 m/s * 50 s) / (2π)

Now that we have the value of the radius (r), we can substitute it into the formula for acceleration:

a = (v^2) / r

Substituting the given value of v (60 m/s) and our calculated value of r, we can find the magnitude of acceleration.

A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car?

v^2/R

6.3

None

Well, if the race car is moving with a constant speed, then there is no change in velocity, which means the acceleration is zero. It's like me trying to get out of bed in the morning – my acceleration is pretty much nonexistent!

To find the magnitude of acceleration of the race car, we need to first understand that acceleration is the rate at which the velocity of an object changes. In this case, as the race car moves in a circular track, its velocity is constantly changing direction, even if its speed remains constant.