course Phy231
4/1/10 8:30am
An object is given an unknown initial velocity up a long ramp on which its acceleration is known to have magnitude 13 cm/s^2..179 seconds later it passes a point 5 cm up the ramp from its initial position.
What are its possible initial velocities, and what is a possible scenario for each?
What is the maximum distance the object travels up the ramp?
a=13cm/s^2 'ds=5cm 'dt=.179s
vAve='ds/'dt=5cm/.179s=27.933cm/s 'dv=a'dt=13cm/s^2*.179s=2.327cm/s Based on these numbers the initial velocity could be
25.606, 30.26cm/s depending on whether the velocity is slowing down or speeding up. I would guess it would be 30.26cm/s and
slowing down because the object is going up hill.
You have the right idea, but `dv is the change between v0 and vf, not the change between v0 and vAve.
The difference between v0 and vAve is half of `dv.
You could have set the problem up with positive acceleration, then with negative acceleration.
The maximum distance based on the initial velocity of 30.26cm/s
v0=30.26cm/s vf=0cm/s a=13cm/s^2
vAve=(0cm/s+30.26cm/s)/2=15.13cm/s 'dv=30.26cm/s-0cm/s=30.26cm/s
'dt='dv/a=30.26cm/s/13cm/s^2=2.328s
'ds=v0'dt+.5adt^2=30.26cm/s*2.328s+.5*13cm/s^2*(2.328s)^2=70.4453+35.227=105.672cm
Good attempt, but see my note for one flaw. In any case you used very good reasoning.
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
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