The sciences concerned with the study of inanimate natural objects, including physics, chemistry, astronomy, and related subjects.
Explanation:
It is given that, the position of a particle as as function of time t is given by :

Let v is the velocity of the particle. Velocity of an object is given by :

![v=\dfrac{d[(8t+9)i+(2t^2-8)j+6tk]}{dt}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bd%5B%288t%2B9%29i%2B%282t%5E2-8%29j%2B6tk%5D%7D%7Bdt%7D)

So, the above equation is the velocity vector.
Let a is the acceleration of the particle. Acceleration of an object is given by :

![a=\dfrac{d[8i+4tj+6k]}{dt}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7Bd%5B8i%2B4tj%2B6k%5D%7D%7Bdt%7D)

At t = 0, 

Hence, this is the required solution.
Answer:
d
Explanation:
In physics and engineering, a free body diagram (force diagram, or FBD) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition.
Answer:
It relaxes
Explanation:
I took the test I hope it helps
Answer:

Explanation:
Given data
Space vehicle speed=5425 km/h relative to earth
The rocket motor speed=81 km/h and mass 4m
The command has mass m
From the conservation of momentum as the system isolated

Since the motion in on direction we can drop the unit vector direction

Where M is the mass of space vehicle which equals to sum of the motors mass and command mass.
The velocity of the motor relative to the earth equals the velocity of the motor relative to command plus the velocity of the command relative to earth

Where Vmc is the velocity of motor relative to command
This yields

Substitute the given values