How to Calculate Velocity

Speed is how fast an object moves in a certain direction. Mathematically, speed is often seen as the change in position of an object over time. This basic concept is present in many physics problems. Which formula should be used depends on what is known of the object, to choose the right formula, read this article carefully.

Table of Contents

Shortened Formula

Average speed = vav=xf−xitf−ti{displaystyle v_{av}={frac {x_{f}-x_{i}}{t_{f}-t_{i}}}} $How to Calculate Velocity$
- $x$ $f$ $=$ ${displaystyle x_{f}=}$ $x_{f}=$ last place $x$ $i$ $=$ ${displaystyle x_{i}=}$ $x_{i}=$ original location
- $t$ $f$ $=$ ${displaystyle t_{f}=}$ $t_{f}=$ last time $t$ $i$ $=$ ${displaystyle t_{i}=}$ $t_{i}=$ initial time
Average velocity when acceleration is constant = vav=vi+vf2{displaystyle v_{av}={frac {v_{i}+v_{f}}{2}}} $v_{{av}}={frac {v_{i}+v_{f}}{2}}$
- $v$ $i$ $=$ ${displaystyle v_{i}=}$ $v_{i}=$ initial velocity $v$ $f$ $=$ ${displaystyle v_{f}=}$ $v_{f}=$ Last velocity
Average velocity if acceleration is constant equal to 0 = $v$ $a$ $v$ $=$ $x$ $t$ ${displaystyle v_{av}={frac {x}{t}}}$ $v_{{av}}={frac {x}{t}}$
Final velocity =vf=vi+at{displaystyle v_{f}=v_{i}+at} $v_{f}=v_{i}+at$
- a = acceleration t = time

Find Average Velocity

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Find the average velocity when the acceleration is constant. If an object has constant acceleration, the formula for average velocity is simple:

v

a

v

=

v

i

+

v

f

2

{displaystyle v_{av}={frac {v_{i}+v_{f}}{2}}}

v_{{av}}={frac {v_{i}+v_{f}}{2}}

. In there,

v

i

{displaystyle v_{i}}

Because}

is the initial velocity, and

v

f

{displaystyle v_{f}}

v_{f}

is the final velocity. Use this formula only if the acceleration is constant.

For example, consider a train with a constant acceleration from 30 m/s to 80 m/s. So the average speed of the train is $30$ $+$ $80$ $2$ $=$ $55$ $m$ $/$ $S$ ${displaystyle {frac {30+80}{2}}=55m/s}$ ${frac {30+80}{2}}=55m/s$ .

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Build formulas using location and time. You can calculate the velocity based on the change in position over time of the object. This method can be applied in all cases. Note that, unless the object is moving at a constant speed, the result you calculate will be the average velocity while moving, not the instantaneous velocity at a certain point in time.

The formula in this case is $v$ $a$ $v$ $=$ $x$ $f$ $-$ $x$ $i$ $t$ $f$ $-$ $t$ $i$ ${displaystyle v_{av}={frac {x_{f}-x_{i}}{t_{f}-t_{i}}}}$ $How to Calculate Velocity$ , i.e. “end position – initial position divided by end time – initial time”. You can also rewrite this formula as $v$ $a$ $v$ ${displaystyle v_{av}}$ $v_{{av}}$ = ^Δx / _Δt , or “change of position over time”.

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Find the distance between the start and end points. When measuring velocity, the only two points to keep in mind are the beginning and the end of the motion. Along with the direction of motion, the starting and ending points will help us determine the displacement or in other words the change in the position of the object under consideration. ^{[1] X Research Source} No need to consider the distance between these two points.

Example 1 : A car traveling east starts at position x = 5 meters. After 8 seconds, the car is at position x = 41 meters. How far has the car moved?
- The car has moved (41m-5m) = 36 meters east.
Example 2 : A diver jumps 1 meter above the jump board, then falls 5 meters before hitting the water. How much has the athlete moved?
- In total, the diver has moved 4 meters below the original position, that is, 4 meters below, or -4 meters in other words. (0 + 1 – 5 = -4). Although the total distance traveled is 6 meters (1 meter up when jumping and 5 meters when falling), the problem lies in the fact that the end of the movement is 4 meters below the starting position.

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Calculate the change in time. How long does it take for the object under consideration to reach its endpoint? There are many exercises that will make this data available. If not given, you can determine by subtracting the start time from the end time.

Example 1 (continued): The problem says that the car takes 8 seconds to get from the starting point to the end, so this is the change in time.
Example 2 (continued): If the athlete jumps at t = 7 seconds and re-waters at t = 8 seconds, change in time = 8 seconds – 7 seconds = 1 second.

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Divide the distance by the travel time. To determine the speed of a moving object, we divide the distance traveled by the total time spent and determine the direction of motion, you will get the average speed of that object.

Example 1 (continued): The car traveled a distance of 36 meters in 8 seconds. We have $v$ $a$ $v$ $=$ $36$ $m$ $8$ $S$ $=$ ${displaystyle v_{av}={frac {36m}{8s}}=}$ $v_{{av}}={frac {36m}{8s}}=$ 4.5 m/s to the east.
Example 2 (continued): The athlete traveled a distance of -4 meters in 1 second. We have $v$ $a$ $v$ $=$ $-$ $4$ $m$ $first$ $S$ $=$ ${displaystyle v_{av}={frac {-4m}{1s}}=}$ $v_{{av}}={frac {-4m}{1s}}=$ -4 m/s . (In one-way motion, a negative number usually implies “downward” or “to the left. In this example, we could give the answer “4 m/s in the downward direction”).

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In the case of two-way motion. Not all exercises involve movement in a fixed line. If the object changes direction at some point, you need to graph and solve geometry problems to find the distance.

Example 3 : A person walks 3 meters east, then turns 90 degrees and walks another 4 meters north. How much has this person moved?
- Draw a graph and connect the start point to the end point in a straight line. We have a right triangle, using the property of right triangles we will calculate the length of its side. In this example, the distance traveled is 5 meters northeast.
- Sometimes the teacher may ask you to find the exact direction of travel (the angle above the horizontal). You can use geometric properties or draw vectors to solve that problem. ^{[2] X Research Source}

Finding Velocity knowing Acceleration

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Formula for the velocity of an accelerated object. Acceleration is the change in velocity. Velocity varies uniformly when acceleration is constant. We can describe this change by multiplying the acceleration times the time then plus the initial velocity:

$v$ $f$ $=$ $v$ $i$ $+$ $a$ $t$ ${displaystyle v_{f}=v_{i}+at}$ $v_{f}=v_{i}+at$ , or “final velocity = initial velocity + (acceleration* time)”
Initial velocity $v$ $i$ ${displaystyle v_{i}}$ $Because}$ sometimes written as $v$ $0$ ${displaystyle v_{0}}$ $v_{0}$ (“velocity at time t = 0”).

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Calculate the product of acceleration and time. The product of acceleration and time shows how much velocity has increased (or decreased) during that time interval.

Example : A train is traveling north with a speed of 2 m/s and an acceleration of 10 m/s ² . How much will the train’s speed increase in the next 5 seconds?
- a = 10 m/s ²
- t = 5 seconds
- Increased velocity (a * t) = (10 m/s ² * 5 s) = 50 m/s.

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Plus initial velocity. Once we know the change in velocity, we add this value to the original velocity of the object to get the required velocity.

Example (continued) : In this example, what is the speed of the train after 5 seconds?
- $v$ $f$ $=$ $v$ $i$ $+$ $a$ $t$ ${displaystyle v_{f}=v_{i}+at}$ $v_{f}=v_{i}+at$
- $v$ $i$ $=$ $2$ $m$ $/$ $S$ ${displaystyle v_{i}=2m/s}$ $v_{i}=2m/s$
- $a$ $t$ $=$ $50$ $m$ $/$ $S$ ${displaystyle at=50m/s}$ $at=50m/s$
- $v$ $f$ $=$ $2$ $m$ $/$ $S$ $+$ $50$ $m$ $/$ $S$ $=$ $52$ $m$ $/$ $S$ ${displaystyle v_{f}=2m/s+50m/s=52m/s}$ $v_{f}=2m/s+50m/s=52m/s$

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Determine the direction of motion. Unlike speed, velocity always accompanies the direction of motion. So remember to always write down the direction of motion when it comes to velocity.

In the example above, since the train is always moving north and doesn’t change direction all the time, its speed is 52 m/s north.

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Solve related exercises. When you know the acceleration and velocity of the object at a certain point in time, you can use this formula to calculate the velocity at any point in time.

Circular Motion Velocity

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Formula for the velocity of circular motion. The velocity of circular motion is the speed an object must achieve to maintain a circular orbit around another body such as a planet or a mass. ^{[3] X Research Sources}

The circular motion of an object is calculated by dividing the circumference of the orbit by the time of motion.
The calculation formula is as follows:
- v = ^(2πr) / _T
Note: 2πr is the circumference of the motion’s trajectory
r is “radius”
T is “motion time interval”

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Multiply the radius of the orbital motion by 2π. The first step is to calculate the circumference of the orbit by taking the product of the radius and 2π. If you don’t use a calculator, you can get π = 3.14.

For example, calculate the speed of circular motion of an object with a radius of 8 meters in 45 seconds.
- r = 8 m
- T = 45 seconds
- Perimeter = 2πr = ~ (2)(3.14)(8 m) = 50.24 m

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Divide the circumference by the time of motion. To calculate the speed of the circular motion of the object in the problem, we divide the calculated circumference by the time of motion of the object.

Example: v = ^(2πr) / _T = ^{50.24 m} / _{45 s} = 1.12 m/s
- The speed of the circular motion of the object is 1.12 m/s.

Advice

Meters per second (m/s) is the standard unit of speed. Double check that the distance is in meters and that the time is in seconds, for acceleration the standard unit is meters per second per second (m/s ² ).

Shortened Formula

Steps

Find Average Velocity

Finding Velocity knowing Acceleration

Circular Motion Velocity

Advice

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