(a)A car travels exactly once around a circle of radius 5.0 m at constant speed of 3.0 m/s. What is the car’s average velocity (magnitude and direction) during this interval? Explain/justify.

(b)Repeat the calculation of average velocity if the car travels halfway around the circle clockwise, if it starts out traveling due north. Make sure to again comment on the meaning of your result! In particular, compare to the speed of the car as it goes around the circular path, and comment.

(a) To find the car's average velocity, we need to determine the displacement and the time it takes for the car to complete one full revolution around the circle.

The displacement of an object is the change in its position, which can be calculated by subtracting the initial position from the final position. In this case, since the car travels once around the circle and returns to its initial position, the displacement is zero.

The time it takes for the car to travel once around the circle can be determined by dividing the circumference of the circle (2πr) by the car's constant speed. Given that the radius of the circle is 5.0 m and the speed is 3.0 m/s, we can calculate the time by dividing 2π(5.0 m) by 3.0 m/s.

Now, the average velocity of an object is defined as the displacement divided by the time it takes to travel that distance. Since the displacement is zero, the average velocity is also zero. Therefore, the car's average velocity is magnitude zero and directionless. This means that the car starts and ends at the same position, and its displacement per unit time is also zero.

(b) If the car travels halfway around the circle clockwise starting from due north, the displacement is half the circumference of the circle. The circumference of the circle is 2πr, so the displacement is (1/2)(2π(5.0 m)), which simplifies to π(5.0 m).

We can calculate the time it takes for the car to travel this distance by dividing the displacement by the car's constant speed. So, π(5.0 m) / 3.0 m/s gives us the time.

To find the average velocity, we divide the displacement by the time taken to travel that distance. The magnitude of the average velocity will be the average speed, which is the magnitude of the displacement divided by the time taken. The average speed is (π(5.0 m)) / (π(5.0 m) / 3.0 m/s).

Simplifying the expression gives us 3.0 m/s, which is the same as the car's constant speed. Therefore, the car's average velocity magnitude when it travels halfway around the circle clockwise starting from due north is equal to its constant speed. The direction of the average velocity will still be in the same direction as the initial direction, i.e., due north. This means that the car is moving in a circular path but with a constant velocity along a straight line.