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 b
at the beginning she is moving toward the left at 4.7 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.
a = m/s²

Explanation:

Step1: Identify initial and final velocities

The positive direction is to the right, so velocity to the left is negative. Initial velocity \( v_i = -4.7 \, \text{m/s} \), final velocity \( v_f = -14.3 \, \text{m/s} \), time \( \Delta t = 12 \, \text{s} \).

Step2: Use acceleration formula

Acceleration \( a = \frac{v_f - v_i}{\Delta t} \). Substitute values: \( a = \frac{-14.3 - (-4.7)}{12} \).

Step3: Calculate numerator

\( -14.3 + 4.7 = -9.6 \).

Step4: Divide by time

\( a = \frac{-9.6}{12} = -0.8 \, \text{m/s}^2 \). Wait, but wait—wait, maybe I misread. Wait, the problem: at beginning, moving left at 4.7 m/s (so \( v_i = -4.7 \)), end moving left at 14.3 m/s ( \( v_f = -14.3 \))? Wait, no—wait, maybe the user made a typo? Wait, no, the image says: "at the beginning she is moving toward the left at 4.7 m/s, and at the end she is moving toward the left at 14.3 m/s". Wait, but then the change in velocity is \( v_f - v_i = -14.3 - (-4.7) = -9.6 \), time 12 s, so acceleration is \( -9.6 / 12 = -0.8 \, \text{m/s}^2 \). But that would be acceleration to the left (negative). Wait, but maybe I messed up the signs. Wait, positive is right, so left is negative. So initial velocity \( v_i = -4.7 \), final \( v_f = -14.3 \). So \( \Delta v = v_f - v_i = -14.3 + 4.7 = -9.6 \, \text{m/s} \). Then \( a = \Delta v / \Delta t = -9.6 / 12 = -0.8 \, \text{m/s}^2 \). Wait, but that's deceleration? No, if moving left faster, acceleration is left (negative). Wait, maybe the problem was supposed to have end moving right? Wait, no, the image says "at the end she is moving toward the left at 14.3 m/s". So the calculation is as above.

Wait, no—wait, maybe I misread the final velocity. Wait, the user's image: "at the end she is moving toward the left at 14.3 m/s". So initial \( v_i = -4.7 \, \text{m/s} \) (left), final \( v_f = -14.3 \, \text{m/s} \) (left). Time \( \Delta t = 12 \, \text{s} \).

Acceleration formula: \( a = \frac{v_f - v_i}{\Delta t} \)

Substitute: \( a = \frac{(-14.3) - (-4.7)}{12} = \frac{-14.3 + 4.7}{12} = \frac{-9.6}{12} = -0.8 \, \text{m/s}^2 \)

Wait, but that's acceleration in the negative direction (left). But maybe the problem had a typo, like end moving right? Wait, no, the image says left. So the answer is -0.8 m/s²? Wait, no, wait—wait, maybe I made a mistake. Wait, let's check again.

Wait, initial velocity: moving left at 4.7 m/s: \( v_i = -4.7 \, \text{m/s} \)

Final velocity: moving left at 14.3 m/s: \( v_f = -14.3 \, \text{m/s} \)

Time interval \( \Delta t = 12 \, \text{s} \)

Acceleration \( a = \frac{v_f - v_i}{\Delta t} = \frac{(-14.3) - (-4.7)}{12} = \frac{-14.3 + 4.7}{12} = \frac{-9.6}{12} = -0.8 \, \text{m/s}^2 \)

So the average acceleration is \( -0.8 \, \text{m/s}^2 \), which means 0.8 m/s² to the left.

Answer:

\( -0.8 \)