- #1
jiboom
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1) a car moves along a straight road against a resistance to motion which is 10 times the speed of the car. the car has a mss of 800kg and the engine is working at the constant rate 5kw. find an expression for the acceleration of the car.
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 I am going wrong on this one!
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 I am going wrong on this one!