Formula for Speed

Definition and calculation of speed

Speed is a physical quantity that can be used to describe the rate of change of position of a body. The speed formula is used in kinematics and classical mechanics.

The SI unit of speed is 1 m/s (metres per second). Other common units of speed are, for example, 1 km/h (kilometre per hour), 1 cm/s (centimetre per second) or 1 kn (1 knot = 1 nautical mile per hour).

Using the formula for speed, you can determine:
- the speed in a uniform rectilinear motion
- the velocity in a uniformly accelerated straight-line motion

The main formula for speed in a uniform rectilinear motion is the ratio of distance to time, which we can describe with the formula: s = d/t, where:
- d = the distance
- t = time
To put it simply, to calculate the average speed with which a body moves, you need to divide the distance travelled (d) by the time (t) in which the body was moving.

An example in which we use the formula for speed.
Calculate the average speed at which a train is moving and which covered a distance of 35km in a time of 0.5h.
Data from the task:
d = 35km
t = 0.5h

Looking for
s = ?
Using the formula for velocity s = d/t, substitute
d= 35/0.5 = 70
s = 70km/h

Answer: According to the speed formula, the train driver covered the distance with an average speed of 70km/h.

The formula for velocity in a uniformly accelerated straight-line motion
In uniformly accelerated rectilinear motion, the speed increases by an equal amount in one second. Note that the acceleration in this motion has a constant value.
Thus, the formula for instantaneous velocity in uniformly accelerated rectilinear motion whose initial velocity is equal to 0 is defined as the relation V = a*t, where:
a = the acceleration,
t = time.

Often in tasks, we need to convert the units that are given in the task. In the formula for velocity, we use the generally known unit conversions such as:
1 km = 1,000m
1 cm = 0.01m
1 nautical mile = 1,852m
1 h = 60s

It is helpful in the speed formula to convert km/h into m/s and vice versa. To convert km/h to m/s, divide the speed value by 3.6. To convert m/s to km/h, multiply the speed value by 3.6.

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