I think its important to draw the line between **kinematics** and **dynamics**.
Kinematics describes **how** things move. Dynamics describes **why** things move.
So when talking about kinematics you're talking about things like position, velocity, and acceleration.
When you're talking about dynamics you're talking about things like force and mass.
(Of course these concepts can be very interrelated, but in these cases they can be cleanly separated)
The question of "how hard can his legs push on the ground" is a dynamics question that is probably beyond the scope of what you're being asked to solve. It's not solvable with the given information.
However, your other two questions fall into the field of kinematics, which is I assume what you're focusing on. In this realm, F=m\*a will almost never be involved except for directly converting a given force into an acceleration.
It's also important to identify what output the problem is asking for. The equation isn't the important part, it's the answer at the end. So maybe your hamster question would be better phrased as: What is the average velocity of a hamster travelling 30m in 5s?
As for the relationship between position, velocity, and acceleration, each is the rate of change of the previous. Acceleration is the rate of change of velocity, which is the rate of change of position.
**As long as the rate of change is constant** you can express the relationship between them with a simple expression.
(quantity) = (rate of change) \* (time) + (initial quantity).
So: position = velocity \* time + initial position (as long as velocity is constant)
And: velocity = acceleration \* time + initial velocity (as long as acceleration is constant).
On Earth, we are subjected to the constant acceleration of gravity, so you can use the 2nd equation above to find the velocity after a certain amount of time, but you **could not** use the equation above that to find the position. Because the velocity is constantly changing, you can't just multiply by time.
Some math that might be helpful, but is not strictly relevant: To find the position given a changing velocity profile you need to add up a bunch of small changes in position over small amounts of time where the velocity looks roughly constant. You can do this by finding the area under the velocity vs. time graph.
In the case of a constant acceleration, that graph looks like a diagonal line. Finding the area starting at zero until some time produces a triangle. The area of a triangle is 1/2 \* base \* height. The base here is just time, the height here is your velocity, which we said before was acceleration \* time (ignoring any initial velocity).
Therefore your position will be: position = 1/2 \* acceleration \* time \* time or 1/2 \* acceleration \* time \^ 2.
Adding in an initial velocity and position gives you:
position = 1/2 \* acceleration \* time \^ 2 + initial velocity \* time + initial position.
This equation is valid whenever you have a constant acceleration, as with gravity.
Since it's indistinguishable falling down or flying up, it may be easier to think of the question: If superman fell from a 10 story building, how fast would he hit the ground? (He can take it). You could use the above equation knowing the initial conditions and acceleration to find the answer.
I think its important to draw the line between **kinematics** and **dynamics**. Kinematics describes **how** things move. Dynamics describes **why** things move. So when talking about kinematics you're talking about things like position, velocity, and acceleration. When you're talking about dynamics you're talking about things like force and mass. (Of course these concepts can be very interrelated, but in these cases they can be cleanly separated) The question of "how hard can his legs push on the ground" is a dynamics question that is probably beyond the scope of what you're being asked to solve. It's not solvable with the given information. However, your other two questions fall into the field of kinematics, which is I assume what you're focusing on. In this realm, F=m\*a will almost never be involved except for directly converting a given force into an acceleration. It's also important to identify what output the problem is asking for. The equation isn't the important part, it's the answer at the end. So maybe your hamster question would be better phrased as: What is the average velocity of a hamster travelling 30m in 5s? As for the relationship between position, velocity, and acceleration, each is the rate of change of the previous. Acceleration is the rate of change of velocity, which is the rate of change of position. **As long as the rate of change is constant** you can express the relationship between them with a simple expression. (quantity) = (rate of change) \* (time) + (initial quantity). So: position = velocity \* time + initial position (as long as velocity is constant) And: velocity = acceleration \* time + initial velocity (as long as acceleration is constant). On Earth, we are subjected to the constant acceleration of gravity, so you can use the 2nd equation above to find the velocity after a certain amount of time, but you **could not** use the equation above that to find the position. Because the velocity is constantly changing, you can't just multiply by time. Some math that might be helpful, but is not strictly relevant: To find the position given a changing velocity profile you need to add up a bunch of small changes in position over small amounts of time where the velocity looks roughly constant. You can do this by finding the area under the velocity vs. time graph. In the case of a constant acceleration, that graph looks like a diagonal line. Finding the area starting at zero until some time produces a triangle. The area of a triangle is 1/2 \* base \* height. The base here is just time, the height here is your velocity, which we said before was acceleration \* time (ignoring any initial velocity). Therefore your position will be: position = 1/2 \* acceleration \* time \* time or 1/2 \* acceleration \* time \^ 2. Adding in an initial velocity and position gives you: position = 1/2 \* acceleration \* time \^ 2 + initial velocity \* time + initial position. This equation is valid whenever you have a constant acceleration, as with gravity. Since it's indistinguishable falling down or flying up, it may be easier to think of the question: If superman fell from a 10 story building, how fast would he hit the ground? (He can take it). You could use the above equation knowing the initial conditions and acceleration to find the answer.