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course PHY 241
Reason out the quantities v0, vf, `dv, vAve, a, `ds and `dt: If an object’s velocity changes at a uniform rate from 9 cm/s to 12 cm/s as it travels 84 cm, then what is the average acceleration of the object?
V0= 9cm/s
Vf= to 12 cm/s
`dv=12-9=3cm/s
vAve=(12+9)/2=10.5cm/s
`ds=84 cm
`dt=
84=(12+9)/2*’dt
84=10.5*dt
Dt=8seconds
A=
12=9+a(8)
3=8a
A=0.375 cm/s^2
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You're using equations here as much as reasoning.
You can reason out average velocity without using an equation.
Having average velocity and displacement you can reason out time interval without the need of an equation.
Having initial and final velocities and time interval you can reason out the acceleration without the need of an equation.
I advocate learning to think in terms of meanings, in addition to being able to use equations. You end up a better problem solver if you can do both.
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Using the equations which govern uniformly accelerated motion determine vf, v0, a, `ds and `dt for an object which accelerates through a distance of 84 cm, starting from velocity 9 cm/s and accelerating at .375 cm/s/s.
V0= 9cm/s
Vf= ?
`ds=84 cm
Dt=?
A=0.375 cm/s^2
ds = v0 `dt + .5 a `dt^2
vf^2 = v0^2 + 2 a `ds
vf^2 = 9^2 + 2 0.375 (84)
vf^2 = 81+ 63
vf^2 = 144
vf=12cm/s
84 = (9 + 12) / 2 * `dt
84 = 10.5 * `dt
`dt=8seconds
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