This is the review I gave Friday. Everyone should go through and answer the review questions
first before taking a look at the answers.
Kinematics
1. What are the 5 variables in kinematics?
2. What is the constant velocity equation?
3. What are the 3 basic kinematics equation?
4. What is the difference between distance and displacement?
5. What is the difference between speed and velocity?
6. What is the difference between velocity and acceleration?
7. Give examples of both positive and negative acceleration.
8. Draw the velocity time graph based on each of the following distance-time graphs. Also
explain the acceleration in each case.
9. What does the area under the curve represent on a velocity-time graph?
10. Describe the motion of freely falling objects. Also, explain the sign for velocity, acceleration
and displacement. Show the velocity-time graph for this situation
11. Describe the motion of a ball as it is launched vertically in the air. Also, explain the sign for
velocity, acceleration and displacement. Show the distance-time graphs Show the velocity-time
graph for this situation.
12. Describe the motion of a ball that is launched horizontally. Include acceleration,
displacement, and velocity in the x and y direction
13. Describe the motion of a ball launched at an angle in the air. Include acceleration,
displacement, and velocity in the x and y direction
14. If a car begins at res and accelerates at a constant rate up to a velocity of 120 m/s. If it takes 6
s for the car to accelerate from rest to 60 m/s, how long does it take for the car to reach 120 m/s,
and how far does the car travel?
15. You are standing on a cliff 30m above the valley floor and throw a watermelon vertically
upward at 3 m/s. How high will the watermelon go above the release height? How long will it
take to hit the ground? What will be the impact velocity when it hits the ground?
16. A ball is launched at a velocity of 25 m/s from a cannon that is 30 degrees above the
horizontal. How far does the ball travel? How long is the ball in the air? What is the maximum
height of the ball?
17. An object is launched straight up at a speed of 50 m/s. What is the maximum height? A. 12.5
m B. 25m C. 125 m D. 250 m E. 1250 m
18. In which one of the following situations does the car have a westward acceleration? A. The
car travels eastward and speeds up. B. The car starts from rest and moves toward the east. C. The
car travels westward and slows down. D. The car travels eastward and slows down. E. The car
travels westward at constant speed.
19. A bomb is released from a plane that is moving upward at 30 degrees from the horizontal.
The speed of the plane is 200 m/s, and the plane has an altitude of 2 km. Determine the
magnitude and direction of the bombs vertical and horizontal components. Determine how long
it takes the bomb to hit the ground. Relative to the horizontal, what angle does the pilot have to
look to see the bomb?
1.
2.
3.
4.
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8.
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a
v0
vf
∆x(also,”s”)
t
v=∆x /t
On your formula chart
Distance is scalar, Displacement is a vector. Distance is the total length of the path traveled.
Displacement is the length of the straight line path from start to end. Pointing in that direction.
Speed is scalar and is distance/time. Velocity is a vector and is displacement/time.
Velocity is a speed with direction, and it is a rate of the change in position over time.
Acceleration is a rate of the change in velocity over time. Speeding up and slowing down are
examples of positive and negative acceleration.
Car moving from rest at a green light. Car braking to a stop at a red light.
Velocity is the derivative or slope of a position versus time curve. The position versus time curve
is straight when velocity is constant and not accelerating, and it is curving up when there is
positive acceleration and curving down when there is negative acceleration.
Area under the curve is equivalent to taking the integral of that curve. The integral of a velocity
curve will give the displacement of the object.
Freely-falling objects are under constant acceleration due to gravity in the vertical direction.
The acceleration of gravity on earth is 9.8 m/s2 or 32.2 ft/s2. At time zero, the initial vertical
velocity has a magnitude (speed) of zero, and the speed of the object increases 9.8 m/s (or 32.2
ft/s) every second.
Answers will vary depending on your positive and negative reference directions. For example, if
down is negative, then the ball initially displaces in the positive direction, and then after its peak
height will begin to travel in the negative direction. Whether its total displacement from the
start of the throw is positive or negative depends on where the ball ends up. Above the start
height, displacement is positive. At the start height, displacement is zero. Below the start
height, displacement is negative. Velocity at the start is positive, at the peak is zero, and going
down is negative. Acceleration due to gravity is pointing down and is negative. The ball is
always under constant negative acceleration in the vertical direction.
When dealing with 2D motion, or projectile motion, one must reference positive and negative
directions for both the horizontal and vertical directions. Remember, the acceleration due to
gravity only affects the vertical direction and has no effect on the ball’s horizontal motion.
Usually, the final horizontal velocity is equal to the initial horizontal velocity.
Remember to separate angled velocities in their x and y components using cos and sin. Be
careful to use the correct trig function. If it gives an angle from the vertical axis, then the
horizontal component of velocity will be defined by cos(90-θ) or simply sinθ.
T = 12 s, ∆x = 720m
s = 0.46m up, t = 2.8s, vf = 24.4 m/s down
total time = 2.55s, max height = 7.97m, sx = 55.21 m
Assuming g=10m/s2, C
D
t = 32.8 s, If the pilot has not changed his trajectory, the bomb will always be directly beneath
him. He would have to look down 90 degrees from the horizontal.
Correction for the Projectile motion worksheet: 7.b. is 1530m, not 4601m
Also, for those that were not here Friday, homework was made due on Monday. Please omit numbers 3
and 4 on the derivatives homework. You will not need to integrate formulas on the test. You will need
to derive velocity and acceleration from position formulas using the power rule.