# Kinematics Aplication problem - variable acceleration.

• Nov 7th 2010, 10:33 AM
Kinematics Aplication problem - variable acceleration.
Hi I need help with this problem.

A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
-40√v, where v is velocity in ft/sec. When will the bullet stop if it enters the sandbag at 950 ft/sec.

Than you.
• Nov 7th 2010, 11:04 AM
mr fantastic
Quote:

Hi I need help with this problem.

A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
-40√v, where v is velocity in ft/sec. When will the bullet stop if it enters the sandbag at 950 ft/sec.

Than you.

Start by setting up an appropriate differential equation. Can you do that?
• Nov 7th 2010, 12:45 PM
Quote:

Originally Posted by mr fantastic
Start by setting up an appropriate differential equation. Can you do that?

I am trying to work with m(dv/dt)=F-kv

dv/dt=950-40v^1/2

Now I can solve this by separation of variables.
Does this make sense.
Thanks
• Nov 7th 2010, 01:00 PM
skeeter
Quote:

A bullet is fired into a sandbag. The acceleration of the bullet within sandbag is
-40√v, where v is velocity in ft/sec.
When will the bullet stop if it enters the sandbag at 950 ft/sec.

*** $\displaystyle \frac{dv}{dt} = -40\sqrt{v}$

separate variables and solve for velocity as a function of time
• Nov 7th 2010, 01:16 PM
*** $\displaystyle \frac{dv}{dt} = -40\sqrt{v}$