Over a time interval of 1.72 years, the velocity of a planet orbiting a distant star reverses direction, changing from +18.2 km/s to -18.8 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 find the difference between the final and initial velocities.
(a) To convert the velocities from km/s to m/s, we multiply them by 1000:
Initial velocity = +18.2 km/s = +18,200 m/s
Final velocity = -18.8 km/s = -18,800 m/s
The total change in velocity is given by:
Total change in velocity = Final velocity - Initial velocity
Plugging in the values:
Total change in velocity = (-18,800 m/s) - (+18,200 m/s)
= -18,800 m/s - 18,200 m/s
= -37,000 m/s
So, the total change in velocity is -37,000 m/s. The negative sign indicates that the velocity is changing in the opposite direction.
(b) To find the average acceleration, we divide the change in velocity by the time interval.
Time interval = 1.72 years
To convert years to seconds, we multiply by the conversion factor:
1 year = 365.25 days (to account for leap years)
= 365.25 * 24 hours
= 365.25 * 24 * 60 minutes
= 365.25 * 24 * 60 * 60 seconds
≈ 31,536,000 seconds
Time interval = 1.72 years * 31,536,000 seconds/year
≈ 54,144,320 seconds
Average acceleration = Total change in velocity / Time interval
Plugging in the values:
Average acceleration = (-37,000 m/s) / (54,144,320 s)
= -0.000682 m/s²
So, the average acceleration during this interval is approximately -0.000682 m/s². The negative sign indicates that the acceleration is in the opposite direction as the initial velocity.