if the wheel on a car accelerates from rest at a constant rate of 1.5rev/s, how fast will it be turning after 3s.
To find the angular velocity (or how fast the wheel is turning) after 3 seconds, we can use the equation:
Angular velocity (ω) = Initial angular velocity + (Angular acceleration × Time)
In this case, the initial angular velocity is 0 because the wheel starts from rest. The angular acceleration is given as 1.5 rev/s², and the time is 3 seconds.
Plugging these values into the equation, we get:
ω = 0 + (1.5 rev/s² × 3 s)
Simplifying the equation, we have:
ω = 4.5 rev/s
Therefore, the wheel will be turning at a rate of 4.5 revolutions per second after 3 seconds.
To find out how fast the wheel will be turning after 3 seconds, we can use the formula for angular velocity:
Angular velocity (ω) = Initial angular velocity (ω₀) + (Angular acceleration (α) × Time (t))
The initial angular velocity (ω₀) is 0 since the wheel starts from rest.
The angular acceleration (α) is given as 1.5 rev/s².
The time (t) is 3 seconds.
Let's calculate the angular velocity after 3 seconds using the formula:
Angular velocity (ω) = 0 + (1.5 rev/s² × 3 s)
Angular velocity (ω) = 4.5 rev/s
Therefore, the wheel will be turning at a rate of 4.5 revolutions per second after 3 seconds.