A car starts from rest and accelerates at a constant rate of 1.1 m/s2. If the radius of the car wheels is 29 cm, and the final angular speed of the car wheel is 48 rad/s, how far does the car travel
The final velocity is
vf = R*w = 0.29*48 = 13.92 m/s. The time spent moving is
Vf/a = 12.65 seconds.
The distance travelled is (Vf/2)*(Vf/a)
Vf^2/(2a)= 1
The "send" button got hit too soon
Vf^2/(2a)= 176 m
To find out how far the car travels, we need to determine the linear speed of the car's wheels and then calculate the distance traveled using that speed.
First, let's convert the radius of the car wheels to meters:
29 cm = 0.29 m
Next, we need to find the initial angular speed of the wheels. Since the car starts from rest, the initial angular speed is 0 rad/s.
Then, we can use the formula for angular acceleration to find the time it takes for the wheels to reach the final angular speed:
Angular acceleration (α) = (Final angular speed (ωf) - Initial angular speed (ωi)) / time (t)
Since the initial angular speed is 0, the formula simplifies to:
Angular acceleration = Final angular speed / time
Given that the final angular speed is 48 rad/s, we need to find the time it takes to reach that speed.
Rearranging the formula, we have:
time (t) = Final angular speed (ωf) / Angular acceleration (α)
Substituting the values, we have:
time (t) = 48 rad/s / 1.1 m/s2
Calculating the time:
time (t) ≈ 43.64 s
Now that we have the time it takes for the car wheels to reach the final angular speed, we can find the linear speed of the wheels. To do this, we use the formula for linear speed (v) in terms of angular speed (ω) and radius (r):
Linear speed (v) = ω * r
Substituting the values, we have:
Linear speed (v) = 48 rad/s * 0.29 m
Calculating the linear speed of the wheels:
Linear speed (v) ≈ 13.92 m/s
Finally, we can calculate the distance the car travels using the formula for constant acceleration:
Distance (d) = (Initial velocity (u) * time (t)) + (0.5 * Acceleration (a) * time (t)2)
Since the car starts from rest, the initial velocity is 0 m/s. The acceleration is given as 1.1 m/s2. The time is 43.64 s, which we calculated earlier.
Substituting the values, we have:
Distance (d) = 0 + (0.5 * 1.1 m/s2 * (43.64 s)2)
Calculating the distance:
Distance (d) ≈ 1061.78 m
Therefore, the car travels approximately 1061.78 meters.