Topic 2 - One-dimensional motion

I. Kinematics is the study of moving objects.

II. Average and instantaneous motion.

A. Distance is a scalar quantity.

B. Displacement is a vector quantity.

C. Average velocity is the change in position (displacement) over a certain period of time.

** v = ∆x/t **

D. Instantaneous velocity is the velocity at a specific moment in time.

E. If an object moves at a constant velocity, average velocity = instantaneous velocity.

F. If an object accelerates at a uniform rate, average velocity will be the average of the initial and

final velocities.

G. Speed is the same as velocity, except that it is scalar.

III. Uniform acceleration.

A. Any time velocity changes, an object is accelerating. ** a = ∆v/t **

1. change in speed

2. change in direction

B. If the velocity changes at a constant rate, the acceleration is uniform.

C. Some equations involving acceleration only apply for objects beginning or ending at rest.

1. ** x = ½ at2 **

2. ** v2 = 2ax **

IV. Acceleration due to gravity has the value of 9.8 m/s2 toward the ground.

Topic 3 – Graphing Motion

V. Graphing motion

A. Displacement (x) vs. time (t).

1. x-axis represents the origin.

2. horizontal line shows an object at rest.

3. direction change on the graph indicates a direction change by the object.

4. slope of the line or curve represents the velocity (remember, v = x/t).

5. parabolic curve shows uniform acceleration.

6. slope of tangent line shows instantaneous velocity.

B. Velocity (v) vs. time (t).

1. object changes direction only when the x-axis is crossed.

2. horizontal line shows a constant velocity.

3. horizontal line at 0 shows an object at rest.

4. sloped line indicates uniform acceleration ( remember, a = v/t).

5. slope of the line or curve represents acceleration.

6. area between the curve and the x-axis represents displacement, since x = vt.

C. Acceleration (a) vs. time (t).

1. horizontal line at the 0 means velocity is constant, however, the object may still be

moving at a constant velocity.

2. horizontal line above the x-axis indicates uniform acceleration in the positive direction

(not necessarily speeding up).

3. horizontal line below the x-axis indicates uniform acceleration in the negative

direction (not necessarily slowing down).

Answers to practice questions:

1. E2. C3. C4. A5. B6. A7. B8. B9. C10. E

Practice Questions

1. A ball is thrown upward with an initial velocity of 20 m/s. How long will the ball take to reach its maximum height?

A. 19.6 sB. 9.8 sC. 6.3 sD. 3.4 sE. 2.0 s

2. A ball is thrown downward from the top of a roof with a speed of 25 m/s. After 2 s, what will its velocity be if up is considered the positive direction?

A. 19.6 m/sB. -5.4 m/sC. -44.6 m/sD. 44.6 m/sE. -25 m/s


Questions 3-5 refer to the velocity vs. time graph shown below.

3. The total distance traveled by the object during the indicated 14 s is closest to...

A. 7.5 mB. 25 mC. 62.5 mD. 77.5 mE. 82.1 m

4. The total displacement of the object during the 14 s indicated is closest to...

A. 7.5 mB. 25 mC. 62.5 mD. 77.5 mE. 82.1 m

5. The average velocity, in meters per second, of the object is closest to...

A. 0B. 0.5C. 2.5D. 4.5E. 5.6


6. What is the total change in velocity for the object whose acceleration versus time graph is given below?

A. 40 m/sB. -40 m/sC. 80 m/sD. -80 m/sE. 0 m/s

7. An object has an initial velocity of 15 m/s. How long must it accelerate at a constant rate of 3 m/s2 before its average velocity is equal to twice its initial velocity?

A. 5 sB. 10 sC. 15 sD. 20 sE. 25 s

*8. An airplane lands on a runway with a velocity of 150 m/s. How far will it travel until it stops if its rate of deceleration is constant at -3 m/s2?

A. 525 mB. 3750 mC. 6235 mD. 9813 mE. 10,435 m

*9. A rocket is propelled upward with an acceleration of 25 m/s2 for 5 s. After that time, the engine is shut off, and the rocket continues to move upward. The maximum height, in meters, that the rocket will reach is... A. 900 B. 1000 C. 1100 D. 1200 E. 1400

*10. A particle moves along the x-axis subject to the following position function: x(t) = 2t2 + 3t -1

What was its average velocity during the interval t=0 to t=3?

A. 2.0 m/sB. 3.3 m/sC. 5 m/sD. 8.3 m/sE. 9.0 m/s