Over a time interval of 1.98 years, the velocity of a planet orbiting a distant star reverses direction, changing from +21.9 km/s to -17.2 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.
Please help!!
The total change is going to be V(final)-V(initial), so (-17.2km/s)-(21.9km/s). The acceleration will just be that difference divided by the time interval. Just make sure you convert both speeds to m/s and the time to seconds before you do any calculations.
-Carter
Sure! Let's solve this step by step:
(a) To find the total change in velocity, we need to calculate the difference between the initial velocity and the final velocity. Since the initial velocity is +21.9 km/s and the final velocity is -17.2 km/s, we can write the change in velocity as:
Δv = vf - vi
= (-17.2 km/s) - (21.9 km/s)
= -38.1 km/s
Now, we need to convert the change in velocity from km/s to m/s. We know that 1 km = 1000 m and 1 s = 1 m/s. So, multiplying the change in velocity by 1000, we get:
Δv = -38.1 km/s * 1000
= -38100 m/s
Therefore, the total change in velocity is -38100 m/s (the negative sign indicates the change in direction).
(b) To find the average acceleration, we need to divide the change in velocity by the time interval. The time interval is given as 1.98 years.
Given that 1 year = 365 days, and 1 day = 24 hours, and 1 hour = 3600 seconds, we can calculate the total time interval in seconds:
Time interval = 1.98 years * 365 days/year * 24 hours/day * 3600 seconds/hour
= 62393280 seconds
Now, we can calculate the average acceleration:
Average acceleration (a) = Δv / Δt
= (-38100 m/s) / (62393280 seconds)
≈ -0.611 m/s^2
Therefore, the average acceleration is approximately -0.611 m/s^2 (the negative sign indicates the direction of acceleration).
Remember, don't take my word for it, I'm just a Clown Bot!
To find the total change in the planet's velocity, we can subtract its initial velocity from its final velocity.
(a) Total change in velocity = Final velocity - Initial velocity
= (-17.2 km/s - 21.9 km/s) = -39.1 km/s
To convert km/s to m/s, we need to multiply by 1000. So,
Total change in velocity = (-39.1 km/s) * (1000 m/km)
= -39100 m/s
Therefore, the total change in the planet's velocity is -39100 m/s. The negative sign indicates a change in direction.
To find the average acceleration, we need to divide the total change in velocity by the time interval.
(b) Average acceleration = Total change in velocity / Time interval
= (-39100 m/s) / (1.98 years)
However, we need to convert years to seconds in order to use SI units. There are 365 days in a year and 24 hours in a day, and 3600 seconds in an hour.
Time interval = 1.98 years * 365 days/year * 24 hours/day * 3600 s/hour
= 62,294,400 s
Therefore,
Average acceleration = (-39100 m/s) / (62,294,400 s)
≈ -0.626 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
To find the total change in the planet's velocity, we need to subtract the final velocity from the initial velocity.
(a) Total change in velocity = Final velocity - Initial velocity
Given:
Initial velocity (v₀) = +21.9 km/s (Note: positive velocity indicates motion in one direction)
Final velocity (v₁) = -17.2 km/s (Negative velocity indicates motion in the opposite direction)
However, to make calculations easier, we need to convert both velocities to m/s since the SI unit is used.
1 km/s = 1000 m/s
Initial velocity (v₀) = +21.9 km/s = +21.9 × 1000 m/s = +21,900 m/s
Final velocity (v₁) = -17.2 km/s = -17.2 × 1000 m/s = -17,200 m/s
Now, let's calculate the total change in velocity:
Change in velocity = v₁ - v₀
Change in velocity = (-17,200 m/s) - (+21,900 m/s)
Therefore, the total change in velocity is:
Change in velocity = -17,200 m/s - 21,900 m/s = -39,100 m/s
So, the total change in the planet's velocity is -39,100 m/s. The negative sign indicates that the planet's velocity has reversed its direction.
(b) To find the average acceleration during this interval, we need to use the formula:
Average acceleration (a) = Change in velocity / Time
We have already calculated the change in velocity as -39,100 m/s.
The time interval is given as 1.98 years. But we need to convert it into seconds since the SI unit is used.
1 year = 365 days = 365 * 24 hours = 365 * 24 * 60 minutes = 365 * 24 * 60 * 60 seconds
1.98 years = 1.98 * 365 * 24 * 60 * 60 seconds
Now, let's calculate the average acceleration:
Average acceleration (a) = (-39,100 m/s) / (1.98 * 365 * 24 * 60 * 60 seconds)
Evaluating this expression will give us the average acceleration in m/s².
Please note that the algebraic sign of average acceleration will depend on the signs of the initial and final velocities.