Influenced by the gravitational pull of a distant star, the velocity of an asteroid changes from from +19.0 km/s to −19.4 km/s over a period of 1.85 years.
(a) What is the total change in the asteroid's velocity? (Indicate the direction with the sign of your answer.)
(b) What is the asteroid's average acceleration during this interval (Indicate the direction with the sign of your answer.)
-36000
(a) To find the total change in the asteroid's velocity, we need to calculate the difference between its initial velocity and final velocity.
Total change in velocity = Final velocity - Initial velocity
Given that the initial velocity is +19.0 km/s and the final velocity is -19.4 km/s, we can calculate the total change in velocity as follows:
Total change in velocity = (-19.4 km/s) - (+19.0 km/s)
= -19.4 km/s - 19.0 km/s
= -38.4 km/s
Therefore, the total change in the asteroid's velocity is -38.4 km/s. The negative sign indicates that the velocity change is in the opposite direction of the initial velocity.
(b) To find the average acceleration, we need to divide the total change in velocity by the time interval.
Average acceleration = Total change in velocity / Time interval
Given that the time interval is 1.85 years, we can calculate the average acceleration as follows:
Average acceleration = (-38.4 km/s) / (1.85 years)
= -20.8 km/s/year
Therefore, the asteroid's average acceleration during this interval is -20.8 km/s/year. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
To find the total change in velocity of the asteroid, we can subtract the initial velocity from the final velocity.
(a) Total change in velocity = final velocity - initial velocity
Given:
Initial velocity = +19.0 km/s
Final velocity = -19.4 km/s
Total change in velocity = -19.4 km/s - (+19.0 km/s)
Total change in velocity = -38.4 km/s
Therefore, the total change in the asteroid's velocity is -38.4 km/s. The negative sign indicates that the velocity decreased.
To find the average acceleration of the asteroid, we can use the formula:
Average acceleration = (Final velocity - Initial velocity) / Time
Given:
Initial velocity = +19.0 km/s
Final velocity = -19.4 km/s
Time = 1.85 years
First, we need to convert the time to seconds because acceleration is in terms of velocity change per unit time.
1 year = 365.25 days (considering leap years)
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
So, 1.85 years = 1.85 * 365.25 * 24 * 60 * 60 seconds
Now, we can substitute the given values into the formula:
Average acceleration = (-19.4 km/s - 19.0 km/s) / (1.85 * 365.25 * 24 * 60 * 60 seconds)
Calculating this expression will give us the average acceleration of the asteroid.
clearly, it is (-19.4 - 19.0)km/s
since acceleration is change in v over time, it is
(-19.4 - 19.0)km/s
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1.85 yr
Of course, that gives a value in units of km/s-yr, probably not one you want to wind up with. Convert yr to seconds, if you want km/s^2