# velocity word problem

• Jan 20th 2011, 07:48 AM
Tweety
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 $\frac{g}{k}$
• Jan 20th 2011, 07:50 AM
Ackbeet
What ideas have you had so far?
• Jan 20th 2011, 11:13 AM
Tweety
Nothing, dont know where to start, should I be using one of the kinematics formula in physics?
• Jan 20th 2011, 11:19 AM
Ackbeet
In both cases, you're essentially asked to solve a first-order differential equation. What equation could you write down for part (a)?
• Jan 21st 2011, 08:06 AM
HallsofIvy
How is velocity related to acceleration?
• Jan 21st 2011, 05:32 PM
Tweety
$V = V_{0} + at$ ?
• Jan 21st 2011, 05:37 PM
skeeter
Quote:

Originally Posted by Tweety
$V = V_{0} + at$ ?

$v = v_0 + gt$

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

$\frac{dv}{dt} = g - kv$
• Jan 22nd 2011, 06:49 AM
HallsofIvy
I was thinking of $\frac{dV}{dt}= a$ but for constant acceleration, that is the same thing. Of course, in this problem, a= -g.
• Jan 22nd 2011, 07:10 AM
skeeter
Quote:

Originally Posted by HallsofIvy
I was thinking of $\frac{dV}{dt}= a$ 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.