Understanding Calculus in Physics: Solving for Varying Acceleration

[daveed]

uhhh... in my physics class we never learned how to deal with acceleration varying =/ so...

there is a 1000kg boat that turns off its engine and starts cruising along at 25m/s. the drag of the boat against the water is directly proportional to the speed v of the boat, where F is in Newtons: F=70v. how long does it take the boat to slow down to 12.5 m/s?

 

[Doc Al]

integrate!

Welcome to PF, daveed!

You'll need a bit of calculus to handle this. Newton's law gives:
$F = ma$, which becomes $-70v = m\frac{dv}{dt}$.
Rewrite it like this: $-70 dt = \frac{m}{v} dv$
Integrate both sides (t = 0, T; v = 25, 12.5) to find the time T.

 

[maverick280857]

The Kinetics/Kinematics course you are taking normally goes consistently with calculus in mathematics. If your physics teacher hasn't mentioned calculus well enough, you might be better off doing some background reading since it plays a very important role in physics. From Doc Al's solution you can easily see how trivial calculus makes your question seem, though it is not always so.

Perhaps a quick intro to differential and integral calculus is a good idea.

Cheers
Vivek