How to find the average speed

Video: How to calculate Average Speed ? IBPs | Bank PO | SSC

Content

Steps
Part 1 of 2: Calculating Average Travel Speed and Time
Part 2 of 2: Calculating Average Speed from Constant Acceleration
Tips
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To calculate the average speed, you need to know the travel value and the total time. Remember that speed is both a numerical value and a direction (so be sure to include direction in your answer). If the problem is given a constant acceleration, calculating the average speed will be even easier.

Steps

Part 1 of 2: Calculating Average Travel Speed and Time

1 Remember that speed is given by both a numerical value and a direction. Velocity describes the rate at which a body’s position changes, as well as the direction in which the body is moving. For example, 100 m / s (south).
- The quantities that are specified both by the numerical value and the direction are called vector quantities... An arrow-shaped icon is placed above the vector values. They differ from scalars, which are purely numerical values. For example, v Is speed.
- In scientific problems, it is recommended to use metric units of measurement for displacement (meters, kilometers, and so on), and in everyday life, use any convenient units of measurement.
2 Find the total displacement, that is, the distance and direction between the start and end points of the path. As an example, consider a body moving at a constant speed in one direction.
- For example, the rocket was launched in a northerly direction and moved for 5 minutes at a constant speed of 120 meters per minute. To calculate the total displacement, use the formula s = vt: (5 minutes) (120 m / min) = 600 m (north).
- If the problem is given constant acceleration, use the formula s = vt + ½at (the next section describes a simplified way of working with constant acceleration).
3 Find the total travel time. In our example, the rocket travels for 5 minutes. Average speed can be expressed in any unit of measurement, but in the international system of units, speed is measured in meters per second (m / s). Convert minutes to seconds: (5 minutes) x (60 seconds / minute) = 300 seconds.
- Even if in a scientific problem the time is given in hours or other units of measurement, it is better to first calculate the speed and then convert it to m / s.
4 Calculate the average speed. If you know the value of displacement and the total travel time, you can calculate the average speed using the formula v_Wed = Δs / Δt. In our example, the average rocket speed is 600 m (north) / (300 seconds) = 2 m / s (north).
- Do not forget to indicate the direction of travel (for example, "forward" or "north").
- In the formula v_Wed = Δs / Δt the symbol "delta" (Δ) means "change in value", that is, Δs / Δt means "change in position to change in time".
- Average speed can be written as v_Wed or like v with a horizontal bar on top.
5 Solving more complex problems, for example, if the body is rotating or the acceleration is not constant. In these cases, the average speed is still calculated as the ratio of the total travel to the total time. It doesn't matter what happens to the body between the start and end points of the path. Here are some examples of tasks with the same total travel and total time (and therefore the same average speed).
- Anna walks west at 1 m / s for 2 seconds, then instantly accelerates to 3 m / s and continues west for 2 seconds. Its total movement is (1 m / s) (2 s) + (3 m / s) (2 s) = 8 m (to the west). Total travel time: 2 s + 2 s = 4 s. Its average speed: 8 m / 4 s = 2 m / s (west).
- Boris walks west at 5 m / s for 3 seconds, then turns around and walks east at 7 m / s for 1 second. We can consider eastward movement as "negative movement" westward, so the total movement is (5 m / s) (3 s) + (-7 m / s) (1 s) = 8 meters. The total time is 4 seconds. Average speed is 8 m (west) / 4 s = 2 m / s (west).
- Julia walks 1 meter to the north, then walks 8 meters to the west, and then goes 1 meter to the south. The total travel time is 4 seconds. Draw a diagram of this movement on paper, and you will see that it ends 8 meters west of the starting point, that is, the total movement is 8 meters. The total travel time was 4 seconds. Average speed is 8 m (west) / 4 s = 2 m / s (west).

Part 2 of 2: Calculating Average Speed from Constant Acceleration

1 Pay attention to the initial speed and constant acceleration. For example: the cyclist starts to move to the right at a speed of 5 m / s and with a constant acceleration of 2 m / s. If the total travel time was 5 seconds, what is the average speed of a cyclist?
- If you don't understand the unit of measure m / s, write it down as m / s / s or as meter per second per second. Acceleration of 2 m / s / s means that the cyclist's speed increases by 2 m / s every second.
2 Find the final speed using acceleration. Acceleration is the rate at which speed changes. You can draw a table and, using the acceleration value, find the final speed at various times. In our example, we want to find the speed at t = 5 s, but we will build a large table to help you understand the process better.
- At the beginning (t = 0), the cyclist rides at a speed of 5 m / s.
- After 1 s (t = 1), the cyclist rides at a speed of 5 m / s + at = 5 m / s + (2 m / s) (1 s) = 7 m / s.
- After 2 s (t = 2), the cyclist rides at a speed of 5 + (2) (2) = 9 m / s.
- After 3 s (t = 3), the cyclist rides at a speed of 5 + (2) (3) = 11 m / s.
- After 4 s (t = 4), the cyclist rides at a speed of 5 + (2) (4) = 13 m / s.
- After 5 s (t = 5), the cyclist rides at a speed of 5 + (2) (5) = 15 m / s.
3 Use the following formula to calculate the average speed. Only if the acceleration is constant, then the average speed is equal to half the sum of the initial and final speeds: (v_n + v_To)/2... In our example, the initial velocity v_n = 5m / s, and the final speed v_To = 15 m / s. The average speed of a cyclist is (15 m / s + 5 m / s) / 2 = (20 m / s) / 2 = 10 m / s (right).
- Do not forget to indicate the direction (in this case "to the right").
- The initial velocity can be denoted as v₀and final as v.
4 Explanation of the formula. To find the average speed, it is necessary to calculate the speed of the body at each time interval, add up the results and divide this sum by the number of time intervals. However, this is long and tedious. Instead, let's find the average speed in just two (any) time frames.
5 Use the above table of final speeds at different points in time. Consider some pairs of time intervals: (t = 0, t = 5), (t = 1, t = 4) or (t = 2, t = 3). Check the process with fractional t values if you like.
- Regardless of which pair of time frames you choose, you will get the same average speed value. For example, (5 + 15) / 2 = (7 + 13) / 2 = (9 + 11) / 2 = 10 m / s (to the right).
6 If we calculated the speed of the body at each time interval, we would get the average speed in the first half of the journey and the average speed in the second half of the journey. Since there are equal number of time intervals in each half, you will not lose a single speed value throughout the entire path (that is, as a result, all speed values will be taken into account).
- Since the average speed remains constant between any two times, the overall average speed is equal to the average speed between any two times.
- We can find the overall average speed by looking at speeds at any two time intervals, for example, start and stop speeds. In our example: (5 + 15) / 2 = 10 m / s (to the right).
7 Mathematical justification of the formula. The following is the mathematical derivation of the formula.
- s = v_nt + ½at (it is more correct to write Δs and Δt).
- Average speed v_Wed = s / t.
- v_Wed = s / t = v_n + ½at
- at = v_To - v_n
- v_Wed = v_n + ½ (v_To - v_n).
- v_Wed = v_n + ½v_To - ½v_n = ½v_n + ½v_To = (v_n + v_To)/2.

Tips

Velocity is different from a "velocity value" because velocity is a vector quantity. Vector quantities are determined by both value and direction, and scalars are determined by value only.
If the body moves forward and backward, you can use positive numbers to represent one direction (for example, forward), and negative numbers to represent movement in the other direction (for example, backward). Write this down at the top of your paper so the instructor understands your calculations.

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