Vocab
This is the rate at which velocity changes
Acceleration
Describe the motion of an object when it reaches the apogee of the graph
The object stops
Ace drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.
-8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2
-8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2
-8.52 m = (-4.9 m/s2) • (t)2
(-8.52 m)/(-4.9 m/s2) = t2
1.739 s2 = t2
t = 1.32 s
The peak height
apogee
Explain how the position time graph of an object thrown directly in the air looks
Chase throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.
(0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d
0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d
(-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2
(-19.6 m/s2) • d = -686.44 m2/s2
d = (-686.44 m2/s2)/ (-19.6 m/s2)
d = 35.0 m
This occurs when an object's motion is determined by gravity alone
Free fall
Prior to the apogee of a position time graph of an object thrown straight in the air, describe the velocity, speed and the acceleration of the object.
velocity in the upward direction as the speed is decreasing, and the acceleration is in the downward direction
Levi takes off in his airplane and it accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.
d = vi*t + 0.5*a*t2
d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2
d = 1720 m
The change in velocity of an object is divided by the change in time
average acceleration
After the apogee of a position time graph of an object thrown straight in the air, describe the velocity, speed and the acceleration of the object.
Velocity in the downward direction, speed is increasing and acceleration in the downward direction
Eli's car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
d = vi*t + 0.5*a*t2
110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2
110 m = (13.57 s2)*a
a = (110 m)/(13.57 s2)
a = 8.10 m/ s2
Acceleration at a given point in time
Rylie is riding the Giant Drop at Great America. If Rylie free falls for 2.60 seconds, what will be her final velocity and how far will she fall?
d = vi*t + 0.5*a*t2
d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s2)*(2.60 s)2
d = -33.1 m (- indicates direction)
vf = vi + a*t
vf = 0 + (-9.8 m/s2)*(2.60 s)
vf = -25.5 m/s (- indicates direction)