##### Math Problems

1. Mercury has a mass of 0.055 times that of Earth, and Jupiter has a mass of 317.8 times that of Earth. How many times is the mass of Jupiter compared to the mass of Mercury?

2. If an object has positive velocity and negative acceleration, is it slowing down or speeding up?

3. Usain Bolt, the world record holder in the 100 and 200 meter races has a PB of 9.58 seconds for the 100 meter. The world record holder for the mile(approximately 1600 meters), run by Hicham El Guerrouj, is 3:43.13. If Usain Bolt ran at the same pace of his 100m world record for 1600 meters, how much faster would he be than Hicham El Guerrouj?

4. If a particle with particle wave-duality has an error in position measurement of 6h, what is the lowest that the error in momentum can be? Note that h refers to planck's constant.

5. Neptune takes about 4 hours to receive the sun and is 30 AU far from the sun. However, Earth is 1 AU away from the sun. How long does it take for the Earth to receive it?

6. If the initial velocity of an object moving on the x-axis is 3 m/s and the velocity of the object at 11s is 4m/s, what is the acceleration of the object at 10.5s?

6b) Adding onto the previous question, assuming that the velocity of the object can

be modeled with the quadratic function v(t) = kt²+(t/22)+c, where k and c are fixed constants. Using context from the previous part, determine the acceleration of the object at 10.5 seconds.

6c) Now, determine when the instantaneous acceleration of the object is equal to the average acceleration of the object on the interval from 0s to 30s.

7. If the position of a ball at a time of x seconds is 6x⁵+5x⁴+4x³+3x²+2x+1, then what is the acceleration of the ball at a time of x seconds?

8. If a truck is moving backwards but is speeding up, is the acceleration positive or negative?