trivial mechanics (1 Viewer)

[OLDMAN]

A particle moves in a straight line subject only to a resistive force proportional to its speed. Its speed falls from 1200 m/s to 800 m/s over 1400 m. Find the time taken to the nearest 0.01 sec.

Note :if writing integrals w/ limits, use notation
I{a--->b}f(x)dx integral upper limit b, lower limit a wrt x

 

[ezzy85]

x^.. = -kv

vdv/dx = -kv

dv/dx = -k

dv = -k dx

I{1200--->800} v dv = I{0--->1400} -kx dx

and then reintegrate using dv/dt and substitute.
is that right?

 

[OLDMAN]

Thats right. Find k and use dv/dt.

Very good. Wanted to find out whether students know how to use integral limits in solving mechanics this way rather than the more cumbersome 2-unit "integrate, add constant and check boundary conditions" way.

ezzy85 passes the test!

 

[OLDMAN]

Quote ezzy85______________________________________________

vdv/dx = -kv

dv/dx = -k

dv = -k dx

I{1200--->800} v dv = I{0--->1400} -kx dx
________________________________________________

Just a correction on your integrals:
I{1200--->800} dv = I{0--->1400} -k dx

As well if you want to be rigorous about the limits, should be
I{1200--->800} dv = I{b--->b+1400} -k dx the b cancels anyway.