Over a time interval of 2.15 years, the velocity of a planet orbiting a distant star reverses direction, changing from +18.9 km/s to -17.3 km/s. Find (a) the total change in the planet's velocity (in m/s) and (b) its average acceleration (in m/s2) during this interval. Include the correct algebraic sign with your answers to convey the directions of the velocity and the acceleration.

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To find the total change in velocity, we need to calculate the difference between the final velocity and the initial velocity.

(a) The total change in velocity can be found by subtracting the initial velocity from the final velocity. Since the units are in km/s, we need to convert them to m/s for consistency.

Final velocity = -17.3 km/s * (1000 m/km) = -17300 m/s
Initial velocity = 18.9 km/s * (1000 m/km) = 18900 m/s

Total change in velocity = Final velocity - Initial velocity
= -17300 m/s - 18900 m/s
= -36200 m/s

So, the total change in velocity is -36200 m/s. The negative sign indicates that the velocity has reversed direction.

(b) Average acceleration is calculated using the formula:
Average acceleration = Change in velocity / Time interval

To find the average acceleration, we need to convert the time interval from years to seconds since the unit for acceleration is m/s^2.

Time interval = 2.15 years * (365.25 days/year) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute)
= 2.15 * 365.25 * 24 * 60 * 60 seconds

Now, we can calculate the average acceleration:

Average acceleration = -36200 m/s / (2.15 * 365.25 * 24 * 60 * 60 seconds)

Calculating this expression will give you the average acceleration in m/s^2. Note that the negative sign indicates the direction of the acceleration, which is opposite to the direction of the initial velocity.