#$&*
course PHY 241
1110pm 11/3/2011
An object is given an unknown initial velocity up a long ramp on which its acceleration is known to havemagnitude 11 cm/s^2. .131 seconds later it passes a point 7.9 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 = +- 11 cm/s^2
t_2 = 0.131 s
x_2 = 7.9 cm
v_ave = 'ds/'dt
= 7.9 cm / 0.131 s
= 60.31 cm/s
a = 'dv/'dt
+- 11 cm/s^2 = 'dv / 0.131 s
'dv = +- 1.441 cm/s
So the change in velocity is 1.4 cm/s, so as long as the initial velocity and the final velocity are within range, v_0 = (v_f - 1.4 cm/s) or v_0 = (vf + 1.4 cm/s)
@& You need to also consider the average velocity, which is about 60 cm/s.*@
The maximum distance the object travels up the ramp is attained when v = 0 cm/s
therefore v_0 = +- 1.4 cm/s
@& This is inconsistent with an average velocity of 60 cm/s.*@
vf^2 = v0^2 + 2 a `ds.
'ds = (vf^2 - v0^2) / (2a)
= (0^2 - 2.8 cm^2/s^2) / -11 cm/s^2
= 0.255 cm
Acceleration must equal -11 cm/s^2 in order to make the change in position positive. The change in position must be positive, because in the problem statement, we assume that 7.9 cm is positive along the x-axis
from the initial starting point. Also, because the object is going up a long ramp, it is slowing, hence the negative acceleration."
@& Good reasoning, except that your assumptions for the last few questions aren't consistent with the correctly calculated average velocity.
Go travel that 7.9 cm in .131 s the object has to start out at a velocity very much higher than 1.4 cm/s.
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