Aspace probe approaches a planet and goes into a low orbit. if the orbiting probe's velocity is vx=−v sin(ωt), vy=v cos(ωt), v = 7.77 103 m/s, ω= 1.20 10-3 radians/s, what is the average magnitude of acceleration of the probe if it remains in orbit for 24 minutes?

here given that the velocity of the probe is

now at initial position where t = 0

Now after t = 24 minutes we need to find final components of velocity

now as we know that acceleration is given as

Now for x direction of motion

Now for y direction of motion

now in order to find the magnitude of acceleration we can say

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas