1. ## velocity word problem

Assume a tomato is in frictionless free fall with a downward velocity v increasing at a constant rate g (g is the gravitational constant). Suppose that the initial velocity is v0 and find a formula for v(t) in terms of
v0 and g.

b) Now introduce a negative term representing air friction that is proportional to the velocity (hence of the form -kv for some constant k). Now find a formula for v(t), Show that as t grows, the velocity approaches the terminal velocity $\displaystyle \frac{g}{k}$

2. What ideas have you had so far?

3. Nothing, dont know where to start, should I be using one of the kinematics formula in physics?

4. In both cases, you're essentially asked to solve a first-order differential equation. What equation could you write down for part (a)?

5. How is velocity related to acceleration?

6. $\displaystyle V = V_{0} + at$ ?

7. Originally Posted by Tweety
$\displaystyle V = V_{0} + at$ ?
$\displaystyle v = v_0 + gt$

to get you started for part (b) ...

$\displaystyle \frac{dv}{dt} = g - kv$

8. I was thinking of $\displaystyle \frac{dV}{dt}= a$ but for constant acceleration, that is the same thing. Of course, in this problem, a= -g.

9. Originally Posted by HallsofIvy
I was thinking of $\displaystyle \frac{dV}{dt}= a$ but for constant acceleration, that is the same thing. Of course, in this problem, a= -g.
I also thought that at the start, but the problem wants the effect of air resistance of the free falling "tomato" to be a negative value (-kv) ... looks like the downward direction is positive in this case.