A car is traveling with a speed of 25 m/s along a straight, horizontal road. Each wheel has a radius of .25 m. If the car speeds up with a linear acceleration of 2.0 m/s^2 for 6.0 s. Find the angular displacement of each wheel during this time in revolutions.

A school bus takes 0:53 hours to reach the schoool from your house. If the average speed of the bus is 19km/h, what is the displacement of the bus during the trip?

To find the angular displacement of each wheel, we need to follow these steps:

Step 1: Calculate the final velocity of the car.
Since the car is traveling with a linear acceleration, we can use the formula: final velocity (v) = initial velocity (u) + (acceleration (a) x time (t)).
Given:
Initial velocity (u) = 25 m/s (given)
Acceleration (a) = 2.0 m/s^2 (given)
Time (t) = 6.0 s (given)

Using the formula, we have:
v = u + (a x t)
v = 25 m/s + (2.0 m/s^2 x 6.0 s)
v = 25 m/s + 12 m/s
v = 37 m/s

Step 2: Calculate the angular velocity of each wheel.
The angular velocity (ω) can be calculated using the formula: angular velocity (ω) = linear velocity (v) / radius (r).
Given:
Linear velocity (v) = 37 m/s (calculated in Step 1)
Radius (r) = 0.25 m (given)

Using the formula, we have:
ω = v / r
ω = 37 m/s / 0.25 m
ω = 148 rad/s

Step 3: Convert the angular velocity to revolutions.
1 revolution is equal to 2π radians. So, to convert angular velocity from radians to revolutions, we can divide the angular velocity by 2π.
Given:
Angular velocity (ω) = 148 rad/s (calculated in Step 2)

Using the formula, we have:
Number of revolutions = ω / (2π)
Number of revolutions = 148 rad/s / (2π)
Number of revolutions ≈ 23.6 revolutions (rounded to one decimal place)

Therefore, the angular displacement of each wheel during this time is approximately 23.6 revolutions.

Car's displacement= S = ut + at^2/2

= 25*6 + 2*6^2/2
= 150 + 36 = 186m
One rev. of wheel covers = 2*pi*r
No. of revolutions = 186/(2*pi*0.25)
= 118.4 rev.