At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle of radius 9.3 m until, at t = 1.38 s, it is traveling east. The car does not alter its speed during the turn.
(a) Find the car's speed.
(b) Find the change in its velocity during the turn.
(c) Find its average acceleration during the turn.
a) The car's speed does not change. They told you that.
b) The speed stays the same but the direction changes by 90 degrees. Draw a vector triangle. The velocity change is the hypotenuse of a 45 degree right triangle.
c) Divide the velocity change vector (from (b)) by the elepased time, 1.38 s
To find the answers to these questions, we need to use some physics equations related to circular motion.
(a) To find the car's speed, we can use the formula for the speed of an object moving in a circle, which is given by:
speed = circumference / time
In this case, the car travels one-quarter of the arc of a circle of radius 9.3 m. The circumference of a circle is given by 2πr, so the distance traveled is (1/4) * 2π * 9.3 m.
The time taken to travel this distance is 1.38 seconds. We can now substitute these values into the formula:
speed = [(1/4) * 2π * 9.3 m] / 1.38 s
Calculating this expression will give us the car's speed in meters per second.
(b) To find the change in velocity during the turn, we need to calculate the initial and final velocities of the car and then find the difference between them. The initial velocity is the velocity of the car when it starts making the turn, and the final velocity is the velocity of the car when it finishes the turn.
Since the car does not alter its speed during the turn, the initial and final velocities have the same magnitude. The initial velocity is directed north, and the final velocity is directed east.
To find the magnitude of the initial velocity, we can use the formula for the speed of an object moving in a circle, as we did in part (a). The magnitude of the initial velocity is the speed when the car starts making the turn.
To find the magnitude of the final velocity, we need to calculate the distance traveled during the turn. We already know the radius of the circle and the angle of the arc (1/4 of a complete circle). Using these values, we can calculate the distance traveled and then divide it by the time taken (1.38 seconds) to get the magnitude of the final velocity.
Finally, we subtract the magnitude of the initial velocity from the magnitude of the final velocity to find the change in velocity during the turn.
(c) To find the average acceleration during the turn, we can use the formula:
average acceleration = change in velocity / time taken
Substituting the values we calculated in part (b) and the time taken (1.38 seconds) into this formula will give us the average acceleration during the turn.