The position of a particle moving along the x axis may be determined from the expression x(t) = btu + ctv, where x will be in me

Kinetic energy is represented as

KE = (0.5) m v²

In each scenario, v = the velocity of the bottle set at  4 m/s

with m = 0.125 kg

KE = (0.5) m v² =  (0.5) (0.125) (4)² = 1 J

for m = 0.250 kg

KE = (0.5) m v² =  (0.5) (0.250) (4)² = 2 J

if m = 0.375 kg

KE = (0.5) m v² =  (0.5) (0.375) (4)² = 3 J

when m = 0.500 kg

KE = (0.5) m v² =  (0.5) (0.500) (4)² = 4 J

Final temperature to determine: Given the following details, the calculations proceed as follows: Mass of the silver ring is m = 4 g, initial temperature is presented, and the heat released is Q = -18 J (indicating heat loss). The specific heat of silver is considered next to find the final temperature.

Let us denote as the highest acceleration of the truck by itself. The force generated by the engine to propel the truck in this scenario is

where m is the mass of the truck alone.

Upon attaching a bus that has double the mass of the truck, the total mass of the entire system (truck+bus) becomes (m+2m)=3m. In this situation, the force generated by the engine is

where a2 represents the new acceleration. 
Since the engine remains unchanged, the force generated stays the same, allowing us to set the force equations equal to each other:

and solving for a2 gives us:

All the weight of the wooden board rests solely on the support situated at the center of the rod, while the other support positioned at one end experiences no reaction force, resulting in a 0 reaction force.

Thus, the reaction force at the central support corresponds to the weight of the board, whereas the end support has 0 reaction force.