Over a time interval of 2.17 years, the velocity of a planet orbiting a distant star reverses direction, changing from +19.3 km/s to -22.9 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.
To find the total change in the planet's velocity, we can subtract the initial velocity from the final velocity:
(a) Total change in velocity = Final velocity - Initial velocity
In this case, the initial velocity is +19.3 km/s and the final velocity is -22.9 km/s. However, we need to convert these velocities to meters per second (m/s) to ensure consistency with the units.
1 km/s = 1000 m/s
So, the initial velocity is +19.3 km/s * 1000 m/s/km = +19300 m/s, and the final velocity is -22.9 km/s * 1000 m/s/km = -22900 m/s.
Substituting these values into the formula, we get:
Total change in velocity = (-22900 m/s) - (+19300 m/s)
Simplifying, we have:
Total change in velocity = -22900 m/s - 19300 m/s
= -42200 m/s
Therefore, the total change in the planet's velocity is -42200 m/s.
Now, let's find the average acceleration during this interval.
(b) Average acceleration = Total change in velocity / Time interval
The time interval given is 2.17 years. To find the average acceleration, we need to convert this time to seconds (s) to match the units of velocity.
1 year = 365.25 days (considering leap years)
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
So, the time interval is:
2.17 years * 365.25 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 68379240 seconds (approx.)
Substituting the values into the formula, we get:
Average acceleration = (-42200 m/s) / 68379240 s
Calculating this expression, we find that the average acceleration is approximately -0.618 m/s^2.
Therefore, the total change in velocity is -42200 m/s, and the average acceleration is approximately -0.618 m/s^2.
To find the total change in velocity, we need to subtract the initial velocity from the final velocity.
(a) The total change in velocity is:
Change in velocity = Final velocity - Initial velocity
Given:
Initial velocity, u = +19.3 km/s
Final velocity, v = -22.9 km/s
To perform the calculation, we need to convert the velocities from km/s to m/s, since the SI unit is meters per second (m/s).
1 km/s = 1000 m/s
Converting the given velocities to m/s:
Initial velocity, u = +19.3 km/s = +19.3 × 1000 m/s = +19300 m/s
Final velocity, v = -22.9 km/s = -22.9 × 1000 m/s = -22900 m/s
Change in velocity = (-22900) - (+19300) = -22900 - 19300 = -42200 m/s
Therefore, the total change in the planet's velocity is -42200 m/s.
(b) To find the average acceleration, we use the formula:
Average acceleration = Change in velocity / Time interval
The given time interval is 2.17 years. However, to use the SI unit for time (seconds), we need to convert this to seconds.
1 year = 365 days (approximately)
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
2.17 years = 2.17 × 365 × 24 × 60 × 60 seconds
Calculating:
2.17 years = 2.17 × 365 × 24 × 60 × 60 seconds = 2.17 × 31536000 seconds = 68311200 seconds
Average acceleration = (-42200) m/s / 68311200 s ≈ -0.618 m/s^2
Therefore, the average acceleration of the planet during this interval is approximately -0.618 m/s^2.