Question

anyone can help me describe how distance ,velocity, accelerations, and energies involved in designing a roller coaster ride.

Answer 1

Well, I'd mention:
\[\Sigma\vec{F}=m\gamma\vec{\alpha}\]
\[\vec{\alpha}=\int\vec{v}dt\]
\[\vec{v}=\int\vec{r}dt\]
\[\frac{\Sigma \vec{F}}{m\gamma}=\vec{\alpha}\]
\[\int\frac{\Sigma \vec{F}}{m\gamma}dt=\vec{v}\]
\[\int\int\frac{\Sigma \vec{F}}{m\gamma}dt=\vec{r}\]
and how all of those would influence how much force needs to be contained by the costers track and all that jazz.

Answer 2

can you explain in words please

Answer 3

Net force = mass * gamma * accel
area under accel/time graph = velocity
area under velocity/time graph = displacement
net force divided by mass*gamma = accel
area under net force divided by mass*gamma/time graph = velocity
area under area under net force divided by mass*gamma/time = displacement

Basically, these are the fundamental relations between these things.
As you increase acceleration, you're increasing the net force (from the first eq), for example.
So if you're making a coaster, if you make it accelerate really fast, you're gonna have to make the track strong enough to withstand the bigger forces.

Answer 4

thanks