Kinematics in One Dimension



Time = t. Scalar. Unit = second (s).



Distance = d. Scalar. Unit = meter (m). The distance is the total amount of ground covered.



Displacement = . Vector. Unit = meter (m).



Average velocity =. Vector. From the definition we see that the units = m/s.

From the definition we see that the magnitude of the average velocity, also called the average speed = (magnitude of the displacement) / Dt. Thus speed is a scalar with units = m/s.

Also from the definition we see that the direction of the average velocity is the same as the direction of the displacement

Instantaneous velocity = . Magnitude of the instantaneous velocity = instantaneous speed.



Average acceleration = . Vector. From the definition we see that the units = .

From the definition we see that the direction of the acceleration is the same as the direction of the change in velocity.

Instantaneous acceleration = .



Now we will.consider cases where the acceleration is constant. Then average acceleration = instantaneous acceleration = .

The five equations of constant-acceleration kinematics:

PROOFS: Use equations 1 & 2 to prove the others. Proofs here.



How to solve a kinematics problem:

  1. List the variables discussed in the problem, both the ones whose values are given and the one whose value you need to find. When you've listed four variables, go to step 2.

  2. Choose one of the five kinematics equations--the one which involves the four variables you wrote down in step 1.

  3. Choose a positive direction. Then plug the givens into your equation and solve for the unknown.



Tricks:

  1. If an object "comes to a halt" then its final velocity is 0.

  2. An object in free fall has a downward acceleration of 9.8 m/s2. COMMON QUESTION: Does that mean the acceleration of a falling body is always negative? Answer: No. The sign of the acceleration depends on which direction you've chosen as positive. If you've chosen "up" to be positive, then the acceleration will indeed be negative. But if you've chosen "down" to be positive then acceleration will be positive. To summarize: in free fall the direction the acceleration is always "down", but the sign of the acceleration may or may not be negative.



Back to main Physics page.

Back to main Science page.

This page maintained by Steven Blatt. Suggestions, comments, questions, and corrections are welcome.