How Speed Is Determined:

In a truck or automobile, speed is determined by the same odometer that measures distance. Though, rather of simply counting up the number of wheel rotations from a given beginning point, a speedometer counts the number of wheel rotations in a given time period. Knowing the wheel circumference, the number of wheel rotations in certain time interval can be translated directly into meters per second.

You know, obviously, that most speedometers respond almost instantly to a change in speed. Such instruments measure the rotation rate of a car or truck axle by the other method, similar to that used by the engine's tachometer (a device which measures revolutions per minute, or rpm). A real-life truck or car speedometer measures instantaneous speed, not average speed. However, if you want to know the average speed you have traveled during a certain time period, you should measure the distance on the odometer and then divide it by the time elapsed.

In a given time period t, when an object travels over a displacement of magnitude q at an average speed v_avg, then the following formulas may apply. These are all arrangements of similar association among the three quantities.

q = v_avgt

v_avg = q/t

t = q/v_avg

PROBLEM:

Look at the graph of figure shown below. The curve A is a straight line. Calculate instantaneous speed v_inst at t =5 seconds?

SOLUTION:

The speed represented by curve A is constant; you can tell since the curve is a straight line. The numbers of meter per second do not change throughout the time duration shown. In 10 seconds, the object travels 20 meters; that is

20 m/10 s = 2 m/s. And hence the speed at t= 5 s is v_inst =2 m/s.