A 625-kg racing car completes one lap in 14.3 s around a circular track with a radius of 55.0 m. The car moves at constant speed.
(a) What is the acceleration of the car?
A 615 kg racing car completes one lap in 14.3 s around a circular track with a radius of 40.0 m. The car moves at constant speed.
(a) What is the acceleration of the car?
To find the acceleration of the car, we can first calculate the car's velocity using the formula for the speed of an object moving in a circular path:
v = (2πr) / t
where v is the velocity, r is the radius of the circular track, and t is the time taken to complete one lap.
Given that the radius of the track is 55.0 m and the time taken to complete one lap is 14.3 s, we can substitute these values into the formula to find the velocity:
v = (2 * π * 55.0) / 14.3
v ≈ 121.72 m/s
Since the question states that the car moves at a constant speed, its velocity is continuous and does not change. This means that the car's acceleration is zero.
Therefore, the acceleration of the car is 0 m/s².
To find the acceleration of the car, we need to use the formula for centripetal acceleration, which is given by:
a = (v^2) / r,
where:
a is the acceleration,
v is the velocity, and
r is the radius.
In this case, we are given the time it takes for the car to complete one lap around the circular track, which is 14.3 seconds. We also know that the car moves at a constant speed, which implies that the velocity remains constant. Therefore, we can find the velocity using the equation:
v = 2πr / t,
where:
v is the velocity,
r is the radius, and
t is the time.
Substituting the given values into the equation, we have:
v = 2 * π * 55.0 m / 14.3 s.
Now, we can calculate the velocity.
v = 2 * 3.14159 * 55.0 m / 14.3 s,
v ≈ 13.55 m/s.
Plugging the value of velocity into the formula for acceleration, we get:
a = (13.55 m/s)^2 / 55.0 m.
Simplifying the equation, we have:
a = 184.02 m^2/s^2 / 55.0 m,
a ≈ 3.347 m/s^2.
Therefore, the acceleration of the car is approximately 3.347 m/s^2.
d = 2pi*r,
d = 6.28*55 = 345.6m = Linear distance,
d = 0.5*at^2 = 345.6 m,
0.5a*(14.3)^2 = 345.6,
102.2a = 345.6,
a = 345.6 / 102.2 = 3.38 m/s^2.