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course Phy 231
3/28 4
An object is given an unknown initial velocity up a long ramp on which its acceleration is known to have magnitude 10 cm/s^2. .123 seconds later it passes a point 6.6 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?
Part 1
'ds = vo*'dt + (1/2)*a*'dt^2
'ds = 'dt(v0 + (1/2)*a*'dt)
'ds/'dt = v0 + (1/2)*a*'dt
v0 = 'ds/'dt - (1/2)*a*'dt
v0 = (6.6 cm / .123 s) - (1/2) * -10 cm/s^2 * .123 s
vO = 54.3 cm/s
Part 2
vf^2 = v0^2 + 2*a*'ds
vf = 0
0 = v0^2 + 2*a*'ds
-vo^2/ 2*a = 'ds
'ds = -(54.3 cm/s)^2 / (2 * (-10 cm/s^2)) = 147 cm
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