How do I find v(t) from v(d)?

[cwb1328]

How do I find the function for velocity with respect to time from an equation for velocity with respect to distance?

The equation of interest is v = 200x / (x+0.5)

I have very limited calculus knowledge (1 and 2) which is really only simple derivatives and integrals, and it’s been a few years as well. Any help and explanations would be appreciated.

If an explanation for the equation is needed (I doubt it), the equation is for velocity (mph) of a vehicle with a top speed of 200mph that reaches 1/2 Vmax in 1/2 mile. That’s what the 200 and 0.5 represent, and x would be distance in miles.

 

[Dr.Peterson]

How do I find the function for velocity with respect to time from an equation for velocity with respect to distance?

The equation of interest is v = 200x / (x+0.5)

If an explanation for the equation is needed (I doubt it), the equation is for velocity (mph) of a vehicle with a top speed of 200mph that reaches 1/2 Vmax in 1/2 mile. That’s what the 200 and 0.5 represent, and x would be distance in miles.

Are you sure this is the right equation for this problem? Please show how you obtained the equation, and what you are assuming. This is necessary, because solving the wrong differential equation is not going to help you.