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. at the beginning of the interval, the astronaut is moving toward the right along the x - axis at 14.3 m/s, and at the end of the interval she is moving toward the right at 4.7 m/s. express your answer in meters per second squared.

Explanation:

Step1: Recall the acceleration formula

Acceleration \( a \) is defined as the change in velocity \( \Delta v \) divided by the change in time \( \Delta t \), so \( a=\frac{\Delta v}{\Delta t}=\frac{v_f - v_i}{t} \).

Step2: Identify initial and final velocities, and time

Initial velocity \( v_i = 14.3\space m/s \), final velocity \( v_f = 4.7\space m/s \), time \( t = 12\space s \).

Step3: Calculate the change in velocity

\( \Delta v=v_f - v_i = 4.7 - 14.3=- 9.6\space m/s \).

Step4: Calculate acceleration

Substitute into the acceleration formula: \( a=\frac{-9.6}{12}=- 0.8\space m/s^2 \). The negative sign indicates the acceleration is in the opposite direction of the positive (right) direction, meaning it's a deceleration (slowing down while moving right).

Answer:

\( -0.8 \)