Question

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right.

(a) At the beginning of the interval, the astronaut is moving toward the right along the x-axis at 15.0 m/s, and at the end of the interval she is moving toward the right at 5.0 m/s.
(b) At the beginning she is moving toward the left at 5.0 m/s, and at the end she is moving toward the left at 15.0 m/s.
(c) At the beginning she is moving toward the right at 15.0 m/s, and at the end she is moving toward the left at 15.0 m/s.

Answer 1

The magnitude, algebraic sign, and direction of average acceleration are determined by finding the difference in velocity and dividing it by the time interval. The algebraic sign indicates whether the acceleration is in the same or opposite direction of motion, and the direction is determined by the positive direction identified.

Step-by-step explanation:

The magnitude of average acceleration can be calculated by finding the difference in velocity and dividing it by the time interval. In interval (a), the astronaut's velocity changes from 15.0 m/s to 5.0 m/s in 10 seconds. So the magnitude of average acceleration is (5.0 m/s - 15.0 m/s) / 10 s = -1.0 m/s². The algebraic sign indicates that the acceleration is negative, meaning it is in the opposite direction of motion. Since the positive direction is to the right, the direction of the average acceleration in interval (a) is to the left.

In interval (b), the astronaut's velocity changes from -5.0 m/s to -15.0 m/s in 10 seconds. So the magnitude of average acceleration is (-15.0 m/s - (-5.0 m/s)) / 10 s = -1.0 m/s². The algebraic sign indicates that the acceleration is negative, meaning it is in the opposite direction of motion. Since the positive direction is to the right, the direction of the average acceleration in interval (b) is to the right.

In interval (c), the astronaut's velocity changes from 15.0 m/s to -15.0 m/s in 10 seconds. So the magnitude of average acceleration is (-15.0 m/s - 15.0 m/s) / 10 s = -3.0 m/s². The algebraic sign indicates that the acceleration is negative, meaning it is in the opposite direction of motion. Since the positive direction is to the right, the direction of the average acceleration in interval (c) is to the left.