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.

Solution 16E The time interval in which she measured her partner’s velocities is 10 s. a) At the beginning of the interval the astronaut is moving toward the right at the speed of 15 m/s. At the end of the interval she was moving toward the right at the speed f 5 m/s. So, the acceleration will be, Vfinal initial515 10 2 acceleration = t = 10 = 10 = 1 m/s . The average acceleration is 1 m/s . the minus sign indicates that she is decelerating and the direction of acceleration is therefore opposite to her velocity. b) At the beginning of the interval the astronaut is moving toward the left at the speed of 5 m/s. At the end of the interval she was moving toward the left at the speed of 15 m/s. So, the acceleration will be, Vfinal initial15(5) 10 2 acceleration = t = 10 = 10 = 1 m/s . The average acceleration is 1 m/s . the minus sign indicates that her direction of motion is towards the negative x-axis. Surely it is accelerating not decelerating. c) At the beginning of the interval the astronaut is moving toward the right at the speed of 15 m/s. At the end of the interval she was moving toward the left at the speed of 15 m/s. So, the acceleration will be, V V acceleration = final init=al15(15)= 30 = 3 m/s .2 t 10 10 2 The average acceleration is 3 m/s . the minus sign indicates that the change in velocity has a direction which is towards the -ve x-axis.