How to Calculate Average Velocity When You Know Position X(T)

Download Article

Download Article

All you lot need to calculate average velocity is the total displacement, or change in position, and the total time. Remember that velocity measures direction too equally speed, so include the direction in your answer, such as "north," "forward," or "left." If the problem involves constant acceleration, you can larn a shortcut that will make finding the solution even easier.

1. one

   Recollect that velocity includes speed and direction. Velocity describes the rate at which an object changes position.^[i] This has to practise with how fast the object is traveling, but also in which management. "100 meters per second south" is a dissimilar velocity than "100 meters per 2nd east."

   • Quantities that include a management are chosen vector quantities'.^[2] They can exist distinguished from directionless or scalar quantities by writing an pointer over the variable. For example, v represents speed, while v ^→ represents velocity, or speed + direction.^[3] If a v is used in this article, information technology refers to velocity.
   • For scientific problems, you should use meters or another metric unit of distance, but for everyday life you tin use whichever unit of measurement yous're comfortable with.

2. two

   Find the total displacement. The displacement is the object'southward alter in position, or the distance and direction between its starting point and terminate indicate.^[4] It doesn't matter where the object moved in before reaching its final position; only the distance betwixt the start point and end betoken matters. For our first example, we'll use an object moving at a constant speed in i direction:

   • Permit'due south say a rocket traveled north for 5 minutes at a constant rate of 120 meters per minute. To calculate its concluding position, use the formula south = vt, or use common sense to realize the rocket must exist at (five minutes)(120 meters/minute) = 600 meters due north of its starting betoken.
   • For problems involving constant acceleration, you could solve for s = vt + ½at², or refer to the other section for a shorter method of finding the reply.

   Advertisement

3. 3

   Find the full corporeality of time spent. In our example problem, the rocket moved forward for v minutes. You lot can express average velocity in any units of time, but seconds are the international scientific standard. We'll convert to seconds in this example: (5 minutes) x (lx seconds/minute) = 300 seconds.

   • Even in a scientific trouble, if the problem uses units of hours or longer periods of fourth dimension, it may exist easier to calculate the velocity, then convert the concluding respond to meters/second.

4. iv

   Calculate boilerplate velocity as displacement over time. If you lot know how far the object traveled, and how long it took to become there, you know how fast information technology was going.^[v] Then for our example, the rocket's average velocity was (600 meters north) / (300 seconds) = ii meters/second n.

   • Think to include the direction (such as "forward" or "north").
   • In formula form, five_av = Δs/Δt. The delta symbol Δ just ways "change in," then Δs/Δt means "change in position over modify in time."
   • Average velocity can be written five_av, or every bit a 5 with a horizontal line over it.

5. 5

   Solve more than complex issues. If an object turns or changes speed, don't become confused. Boilerplate velocity is even so calculated only from the total displacement, and the full fourth dimension. It doesn't matter what happens in betwixt the start point. Here are a few examples of journeys with the exact aforementioned displacement and time, and therefore the same average velocity:

   • Anna walks west at 1 k/southward for 2 seconds, then instantly accelerates to 3 m/due south and keeps walking west for 2 seconds. Her total displacement is (1 g/s west)(2 s) + (3 thousand/s due west)(2 s) = 8 meters westward. Her total time is 2s + 2s = 4s. Her average velocity is 8m west / 4s = 2 m/s w.
   • Bart walks west at 5 1000/s for three seconds, then turns effectually and walks e at 7 m/s for 1 2nd. We tin treat the e movement as "negative motion west," then total displacement = (5 m/southward west)(iii s) + (-7 thou/s westward)(one southward) = eight meters. Total time = 4s. Average velocity = 8 m w / 4s = 2 thou/s west.
   • Charlotte walks n 1 meter, so walks west 8 meters, and then due south one meter. It takes her 4 seconds total to walk this distance. Depict a diagram on a piece of paper, and you'll see that she ends upward 8 meters west of her starting indicate, so this is her deportation. Total fourth dimension is 4 seconds again, then the average velocity is still 8 m west / 4s = 2 grand/south west.

   Advertisement

1. ane

   Annotation the initial velocity and abiding acceleration. Let'due south say your trouble is "The bike begins traveling to the right at five m/s, constantly accelerating at 2 m/s^two. If it travels for 5 seconds, what is its average velocity?"

   • If the unit "1000/due south²" makes no sense to yous, write it equally "m/s/southward" or "meters per second per second."^[6] An dispatch of 2 one thousand/south/s means the velocity increases by ii meters per 2d, each 2nd.

2. 2

   Apply acceleration to find the final velocity. Acceleration, written a, is the rate of change in velocity (or speed).^[7] The velocity is rising at a constant charge per unit of increase. You can depict a table using the acceleration to find out the velocity at different moments during this journeying. Nosotros'll need to do this for the final moment in the trouble (at t = 5 seconds), merely nosotros'll write a longer table to assist y'all grasp this concept:

   • At the beginning (time t = 0 seconds ), the wheel is traveling correct at 5 m/south.
   • After 1 second (t = 1), the bike moves at 5 m/s + at = v 1000/south + (2 m/southward²)(i due south) = 7 m/due south.
   • At t = 2, the bike is moving correct at 5+(two)(2) = 9 m/s.
   • At t = iii, the bike is moving right at 5+(ii)(3) = 11 1000/s.
   • At t = four, the bike is moving right at 5+(2)(iv) = 13 m/s.
   • At t = 5, the bike is moving right at 5+(2)(5) = xv one thousand/southward.

3. iii

   Utilize this formula to find average velocity. If and simply if the acceleration is constant, the average velocity is the same as the average of the terminal velocity and the initial velocity: (five_f + 5_i)/2. For our example, the bike's initial velocity v_i is 5 m/s. As nosotros worked out higher up, it ends up traveling at a final velocity v_f of fifteen m/s. Plugging these numbers in, we get (15 yard/southward + 5 1000/s) / ii = (xx m/s) / 2 = 10 m/due south right.

   • Call up to include the direction, in this case "right."
   • These terms tin instead be written as v₀ (velocity at time 0, or initial velocity), and simply 5 (final velocity).

4. 4

   Sympathize the average velocity formula intuitively. To discover the average velocity, we could take the velocity at every single moment and discover the boilerplate of the unabridged list. (This is the definition of boilerplate.) Since that would require calculus or infinite time, let's build off of this for a more intuitive explanation instead. Instead of every moment in time, let'southward accept the average of the velocity at only two points in time and encounter what we get. One point in time volition be virtually the beginning of the journey, when the bike is traveling slow, and the other will be equally close to the end of the journey, when the bike is traveling fast.

5. v

   Test out the intuitive theory. Employ the table higher up for the velocities at different points in time. Some of the pairs that fit out criteria are at (t=0, t=v), (t=i, t=4), or (t=2, t=3). You can test this with non-integer values of t as well, if you like.

   • No matter which pair of points we choose, the average of the two velocities at those times will always be the same. For example, ((5+fifteen)/2), ((7+thirteen)/2), or ((9+xi)/ii) all equal 10 m/southward right.

6. 6

   Finish the intuitive explanation. If we used this method with a list of every moment in fourth dimension (somehow), we would proceed averaging 1 velocity from the first one-half with one velocity from the second one-half of the journey. There's an equal corporeality of time in each one-half, and then no velocities would be unaccounted for after we were finished.

   • Since whatever i of these pairs boilerplate to the aforementioned amount, the average of all these velocities will exist equal to this amount. In our example, the boilerplate of all of those "10 1000/s correct" will withal be ten m/s correct.
   • Nosotros can detect this corporeality by averaging any one of these pairs, for instance the initial and final velocities. In our example, those are at t=0 and t=5, and can exist calculated using the formula to a higher place: (v+fifteen)/ii = 10 m/due south right.

7. vii

   Understand the formula mathematically. If you lot're more comfortable with a proof written every bit formulas, you can offset with the formula for altitude traveled assuming abiding acceleration, and derive this formula from there:^[8]

   • south = v_it + ½atⁱⁱ. (Technically Δs and Δt, or modify in position and change in time, but yous'll be understood if you use s and t.)
   • Average velocity five_av is defined equally s/t, so allow's put the formula in terms of s/t.
   • v_av = s/t = v_i + ½at
   • Acceleration x time equals the total modify in velocity, or v_f - v_i. So we tin replace "at" in the formula and get:
   • v_av = v_i + ½(5_f - v_i).
   • Simplify: v_av = v_i + ½v_f - ½v_i = ½5_i + ½5_f = (five_f + five_i)/2.

   Advert

Add New Question

• Question

  How practice I find the average velocity?

  

  Average velocity is the deportation divided by the time interval in which the deportation occurs . Therefore five= ∆x÷∆t.

• Question

  How would the momentum of the commuter'due south car organisation modify if the velocity remained unchanged but another person was in the car?

  

  P=MV. Momentum depends on the mass of the body. Even if the velocity remains unchanged, if the mass of the car varies with the addition of another person, the momentum of the automobile changes.

• Question

  A taxi starts from rest and moves with a constant acceleration of 4m/due south squared. Calculate the average velocity later five seconds. What'due south the answer to this question?

  

  After 5 seconds, the taxi will have a speed of iv/ms^2 x 5 s = 20 yard/due south. The average speed is 20 thou/s / two = x k/s, because the speed increases from 0 m/due south to xx chiliad/s in a straight line -- in such a example, the average speed is the maximum speed divided by 2. In general, Vavg is the integral of V with respect to t from Vinitial to Vfinal divided past tfinal - tinitial. In this case, V = 4t m/southward, so the integral wrt t is 2t^ii, which gives 2 x 25 = 50 grand, divided by five s, = ten k/s.

• Question

  600m every bit the total displacement, the time and speed are 5 seconds and 20m/s. How can I summate the average speed?

  

  Seconds * Meters Per Seconds, so in this case: 5 * 20 = 100 100 is boilerplate speed.

• Question

  The dancer moves 4 meters to the right stage in 10 sec. What is his average velocity?

  

  Average Velocity = Total Deportation / Full time = 0.4 m/s

• Question

  How practise I detect velocity if speed is given?

  

  Follow the instructions listed in the article above.

• Question

  How practise I find the boilerplate velocity of two different moving objects?

  

  Cabbache

  Community Reply

  Add together up their velocity and divide the sum by 2. If you lot had 3 objects, exercise the same only divide by 3.

Inquire a Question

200 characters left

Include your electronic mail address to become a message when this question is answered.

Submit

Advertisement

Video

• Velocity is dissimilar from speed because velocity is a vector quantity and speed is a scalar quantity. Vector quantities prove direction too every bit magnitude, while scalar quantities testify only magnitude.

• If the object only moves in one dimension, such every bit left-right, y'all can apply positive numbers to represent ane direction (such as right), and negative numbers in the other (left). Write this down at the top of the page so it's articulate to people reading your piece of work.

Thanks for submitting a tip for review!

Advertisement

Nearly This Article

Article Summary 10

To calculate average velocity from displacement and time, first detect the total displacement, which is the distance and direction between the starting and ending points. And so discover the full amount of time spent, and convert information technology to seconds, which are the international scientific standard. Finally, calculate average velocity as displacement over time past dividing the total displacement by the total amount of time. Be sure to include the management, like "forrard" or "northward," in your respond. For more information on computing average velocity, including when you have abiding acceleration, scroll downwards!

Did this summary assistance you?

Thanks to all authors for creating a folio that has been read 677,871 times.

Did this article help you?

marchanaporder.blogspot.com

Source: https://www.wikihow.com/Calculate-Average-Velocity

Share this post