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!

change = -17.2 -21.9 = -39.1 *10^3 m/s

a = change in velocity/change in time

change in time
=1.98y(365d/y)(24h/d)(3600s/h)
=6.244128 *10^7 seconds
so
a = -3.91*10^4/6.24*10^7
= - 6.26*10^-4 m/s

To find the total change in velocity, we need to calculate the difference between the initial velocity and the final velocity. Given that the initial velocity is +21.9 km/s and the final velocity is -17.2 km/s, we can subtract the final velocity from the initial velocity to find the total change.

(a) Total change in velocity = final velocity - initial velocity
= -17.2 km/s - (+21.9 km/s)

To perform this subtraction, we can convert both velocities to the same unit. Let's convert them to meters per second (m/s) by multiplying by 1000.

1 km/s = 1000 m/s

So, multiplying the velocities by 1000:

Initial velocity = +21.9 km/s × 1000 = +21,900 m/s
Final velocity = -17.2 km/s × 1000 = -17,200 m/s

Now, we can substitute these values back into the equation:

(a) Total change in velocity = -17,200 m/s - (+21,900 m/s)
= -17,200 m/s - 21,900 m/s

Subtracting the two values, we get:

Total change in velocity = -39,100 m/s

Therefore, the total change in the planet's velocity is -39,100 m/s. The negative sign indicates that the velocity has reversed direction.

To find the average acceleration, we can use the formula for average acceleration:

Average acceleration = Total change in velocity / Time interval

The time interval in this case is given as 1.98 years. Since acceleration is a rate of change of velocity over time, we should convert the time interval to seconds.

1 year = 365.25 days (on average, accounting for leap years)
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

So, multiplying the time interval by these conversion factors:

Time interval = 1.98 years × 365.25 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute

Calculating this expression will give us the time interval in seconds.

(b) Average acceleration = Total change in velocity / Time interval

Now we can substitute the values we found:

Average acceleration = -39,100 m/s / Time interval (in seconds)

Calculating the time interval expression:

Time interval = 1.98 years × 365.25 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute

After evaluating the time interval, we can substitute it back into the average acceleration formula to find the answer.