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 12 s interval. what is the average acceleration in each interval? assume that the positive direction is to the right.

part c

at the beginning she is moving toward the right at 14.3 m/s, and at the end she is moving toward the left at 14.3 m/s. express your answer in meters per second squared.

Explanation:

Step1: Define acceleration formula

Acceleration \( a \) is the change in velocity \( \Delta v \) over time \( \Delta t \), so \( a = \frac{\Delta v}{\Delta t} \).

Step2: Determine initial and final velocities

Initial velocity \( v_i = 14.3 \, \text{m/s} \) (right, positive). Final velocity \( v_f = -14.3 \, \text{m/s} \) (left, negative).

Step3: Calculate change in velocity

\( \Delta v = v_f - v_i = -14.3 - 14.3 = -28.6 \, \text{m/s} \).

Step4: Calculate acceleration

Time \( \Delta t = 12 \, \text{s} \). So \( a = \frac{-28.6}{12} \approx -2.38 \, \text{m/s}^2 \). The negative sign indicates acceleration to the left.

Answer:

\( -2.38 \, \text{m/s}^2 \) (or approximately \( -2.4 \, \text{m/s}^2 \) depending on rounding)