At t = 0, an automobile traveling north begins to take a turn. It follows one-quarter of the arc of the circle of radius 9.8 m until, at t = 1.38 sec, it is traveling east. The car does not alter its speed during the turn.
and then what? runs out of gas? breaks an axle? gets hit by a semi?
Now, if you want the car's speed during the turn, that would be
pi/2 * 9.8 m/1.38s = 11.2 m/s
To determine the speed of the automobile during the turn, we can use the concept of angular velocity.
The first step is to find the angle through which the automobile turns during the given time interval. Since it takes one-quarter of the arc of a circle, it means the car has turned 90 degrees.
Next, we can calculate the angular displacement using the formula:
θ = ωt
Where:
θ is the angular displacement in radians,
ω is the angular velocity in radians per second,
t is the time in seconds.
In this case, θ = 90 degrees = π/2 radians, and t = 1.38 seconds.
Substituting these values into the formula, we can solve for the angular velocity ω:
π/2 = ω * 1.38
Solving this equation for ω, we find that ω ≈ 2.29 radians per second.
Now, we know that angular velocity is related to linear velocity by the formula:
v = ω * r
Where:
v is the linear velocity in meters per second,
ω is the angular velocity in radians per second,
r is the radius of the circle.
In this case, the radius of the circle is given as 9.8 meters.
Substituting the values of ω and r into the formula, we can calculate the linear velocity v:
v = 2.29 * 9.8
Calculating this, we find that the linear velocity of the automobile during the turn is approximately 22.47 meters per second.