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my attempt:

P=driving force.v => 5000/v=driving force

f=ma=>800a=5000/v-10v =>a=50/8v -v/80

book answer is 5/v-v/80

2) a particle leaves a point A at time t=0 with speed u and moves towards a point B with retardation Lv,where v is the speed of the particle at time t. the particle is at a distance s from A at time t.

i have then shown:

v=u-Ls................(1)

ln(u-Ls)=ln u-Lt.....(2)

at t=o a second particle starts from rest at B and move towards A eith accel 2+6t. the particles collide at the midpoint of AB when t=1. find the distance AB and the speeds of the particles on impact.

here i found AB=4 and speed of particle from B is 5 to the left.

for speed of A i have used (1) (2) with t=1 s=(AB/2)=2

(2) gives ln(u-2L)=lnu-L

L=ln(u/u-2L)

e^L=u/u-2L

u=-2L/(1-e^L)

then (1) gives

v=u-2L

=-2L[{1/(1-e^l)}+1]

=-2L/(1-e^L)[1+1-e^L]

=2L{e^L-2}/(1-e^L}

but book gives

-2L(1-e^L}

3)

a disc is set spinning and turns through T degrees in t seconds where

T=120t-6t^2,

calculate the rate in revolutions per minute,at which the disc is rotating when t=6

im saying (guesing)

T=(120t-6t^2)∏/180 gives me T in radians

DT/dt=ω=(120-12t))∏/180

when t=6,

ω=48∏/180 rads/6 secs

so revs per min =

2∏*10/(48∏/180)

=1800/24=75

but books says 8.

im sure im going wrong on this one!!