when given the function:
v = 100( 9.8 - e^(t/-100)
how can i get a displacement function?
that is, i need a function of displacement with respect to velocity
Are we to assume that v is a velocity function? If so then $\displaystyle v= \frac{dx}{dt}$ where x is the displacement function. To go from v to x, you need to "reverse" the derivative which means find the anti-derivative or integral. Integrating this directly will give x as a function of t. But it is not too hard to solve the given equation for t as a function of v and then just replace t.
Two other points: your formula is missing a right parenthesis ")" so it is a little ambiguous. "Displacement" means distance from a specific point. What specific point are you talking about? The position at t= 0? Since integrating will introduce a "constant of integration", you will need to know that to find a value for the constant.
hey,
yes i can simply integrate this velocity function to get a displacement function However, i need this displacement function to be with respect to velocity rather than time.
the ')' is missing from the end of the equation, my mistake.
i am not sure how to get this displacement function to be a function of velocity rather than time.
yes the displacement will be from t=0. on the whole i am trying to determine the final velocity of an object falling 15 metres with negligible initial velocity and a wind resistance of 0.01v. so once i have a displacement function i can determine this
thanks