Average Speed

The average speed of an object is defined as the entire distance it goes divided by the amount of time that has elapsed since it started. 

Because it is defined solely by a magnitude, the average speed is unquestionably a scalar quantity.

Average Speed

The average speed is calculated using the following formula:

Average Speed = Total distance covered throughout the journey

Total time taken for the journey

The distance travelled by a particle at a constant speed is equal to its average speed multiplied with time. The elapsed time is the amount of time it took the object to travel the entire distance.

A moving item will often travel at various speeds over a given distance. Consider the case of an automobile moving from one city to another, which will seldom maintain a consistent pace. While driving, it is more probable that the car’s speed will change throughout the journey. The automobile may cruise at 65 mph for a short period before slowing down to 25 mph. It is conceivable that the automobile will come to a complete halt at some points (such as at a red light). When calculating the average speed of the automobile, we aren’t concerned with the oscillations in its speed. We are only concerned with the overall distance travelled by automobile and its time to cover that entire distance.

Average Speed Formula

The following is the formula for average speed:

Average Speed = Total distance covered throughout the journey

Total time taken for the journey

This formula is similar to the formula for constant speed. The average speed is measured in the distance travelled per unit of time. Miles per hour (mph), kilometres per hour (kmph), metres per second (m/s) and feet per second (ft/s) are some of the most often used units of speed.

The average speed of your brand-new red sports automobile, according to your friend’s assessment, was perfect! He divided the distance travelled by car (45 miles) by the time elapsed (1.25 hours). The work on the highway, as well as a slew of red lights on the side roads, significantly hampered your progress. As a result of the long elapsed period, the average speed was low. Mistakes and assumptions that are often made while calculating the same are defined in the next section.

Misconceptions about Average Speed

The average speed doesn’t need to have the same magnitude as the average velocity. Average speed and average velocity are two distinct names for the same quantity. However, average speed relies on distance, and average velocity depends on displacement. Average speed and average velocity are not the same things. 

Suppose an object changes direction throughout its travel. In that case, the distance will be larger than the displacement, and the average speed will be more than the magnitude of the average velocity.

Average speed is a scalar quantity, but average velocity is a vector quantity. When the displacement is in the negative direction, the average velocity reflects the direction of the displacement and can be expressed as a negative number. In contrast to average velocity, which indicates direction, the average speed can only be positive or zero.

Problems on Average Speed 

Example 1: Using the average speed method, calculate Ria’s average speed for the first 10 km in four hours and the next 16 km in another six hours.

Solution:

The whole distance and total time are required to calculate the average speed.

Ria’s total distance travelled = 10 km + 16 km = 26 km

Ria’s total time is 4 hours + 6 hours = 10 hours.

Average Speed = Total Distance Travelled/ Total Time Spent

Average Speed = 26/10 = 2.6 km/h

Ria’s average speed is 2.6 kilometres per hour.

Example 2: A train is moving  at a speed of  120 km/h for the first four hours and then at a speed of 100 km/h for the remaining two hours. Using the average speed formula, determine the train’s average speed.

Solution:

In this case, S1 = 120 km/h and T1 = 4 h.

And the train will be travelling at 100 km/h for the next two hours.

Hence

S2 = 100 km/h and T2 = 2h.

Average Speed Formula =  (S1T1 + S2T2 ) / T1 + T2

Average Speed = (120x 4 + 100x 2)/(4 + 2) = (680)/(6) = 113.33 km/h

The train’s average speed is 113.33 km/h.

Example 3: A car moves at a speed of 30 km/hr for 2 hours and then slows down to 20 km/hr for next 1 hour. Find the average speed of the car.

Solution:

Distance 1 = 30x 2 = 60 km 

Distance 2 = 20x 1 =20 km

Distance total = Distance 1 + Distance 2 

D = 60 + 20 = 80 km

Total distance travelled / Total time taken =  Average Speed = 80/3 = 26.67 km/hr

Summary

The mean value of a body’s speed over time is referred to as its average speed. Because the speed of a moving body is not constant and changes over time, the formula for average speed becomes necessary. Even though the speed varies, the values of total time and total distance travelled may be utilised to describe the motion. With the aid of the formula for average speed, we can obtain a single number to represent the full motion using the average speed formula.