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Speed or Velocity?

Speed is the rate of motion, or the rate of change of position. It is expressed as distance moved (d) per unit of time(t). Speed is a scalar quantity with dimensions distance/time. Speed is measured in the same physical units of measurement as velocity, but does not contain an element of direction. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components.

Common speeds of moving objects

For human beings, an average walking speed is about 3 mph (~5 km/h, 1.39m/s),
The speed of long distance jogging for average persons is about 6 mph (~10 km/h, 2.7 m/s).
Top athletic sprinters can run at 23.03 mph (~36.85 km/h, 10.24 m/s) within a short distance such as a 200 meters dash.
Cycling can average 12 mph (~20 km/h, 5.56 m/s)
Car can average 65 mph (~104 km/h, 28.9 m/s ) on highway
747 Airplane has an average speed 565 mi/hr


Acceleration, (symbol: a) is defined as the rate of change of velocity. It is thus a vector quantity with dimension length/time˛. In SI units, acceleration is measured in meters/second˛.

To accelerate an object is to change its velocity, which is accomplished by altering either its speed or direction (like in case of uniform circular motion) in relation to time. Acceleration can have positive and negative values. Any time that the sign (+ or -) of the acceleration is the same as the sign of the velocity, the object will speed up. If the signs are opposite, the object will slow down. Acceleration is a vector quantity. When either velocity or direction changes, there is acceleration (or deceleration).

To accelerate an object requires the application of a force.

Graphing Velocity and Acceleration

A car accelerates from rest. The following two graphs are created using a java applet (see below).

The graph of velocity (m/sec.) vs. time (sec.) is a straight line for accelerating objects.

acceleration = velocity / time

What is the slope of this graph?

Please enter your answer in the space provided:


The graph of distance (x) vs. time (t) is a curve where the equation of motion is:

x = 1/2 at˛. What value of (a) would you expect for this graph?

Hint: For each value of t (in s), there is only one value for x (in m). Pick any ordered pair for t and x and substitute them into the above equation. Then solve for a.


Create your own graphs for accelerating objects using the following java applet:   This Java applet shows a car moving with constant acceleration. The green control panel contains text fields where you can vary the values of initial position, initial velocity and acceleration (don't forget to press the "Enter" key!). By using the buttons at the top right you can bring back the car to its initial position or stop and resume the simulation. The diagrams illustrate the motion of the vehicle: Position x versus time t Velocity v versus time t Acceleration a versus time t





This is an excellent laboratory exercise for Middle and High School students:

Problem: What is the relationship between the distance an accelerating object travels and the time it takes to travel that distance?

Test your Understanding:

1. The units for acceleration are:
a) m/sec
b) m/sec˛
c) sec
d) (m/sec)˛

2. Which of the following are true about acceleration?
a) Acceleration is a change in velocity
b) An applied force is required for acceleration to occur
c) Acceleration can be either + or - in value.
d) All of the above

3. In the graph shown above for an accelerating object, the acceleration is closest to?
a) 1 meters/second˛
b) 2 meters/second˛
c) 3 meters/second˛
d) 4 meters/second˛

4. The units for velocity are:
a) m/sec˛
b) sec.
c) miles
d) m/sec

5. The slope of the graph of velocity vs. time (x-axis, velocity; y-axis, time) is:
a) distance
b) acceleration
c) speed

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