Quantities that include a direction are called vector quantities’. [2] X Research source They can be distinguished from directionless or scalar quantities by writing an arrow over the variable. For example, v represents speed, while v→ represents velocity, or speed + direction. [3] X Research source If a v is used in this article, it refers to velocity. For scientific problems, you should use meters or another metric unit of distance, but for everyday life you can use whichever unit you’re comfortable with.
Let’s say a rocket traveled north for 5 minutes at a constant rate of 120 meters per minute. To calculate its final position, use the formula s = vt, or use common sense to realize the rocket must be at (5 minutes)(120 meters/minute) = 600 meters north of its starting point. 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 answer.
Even in a scientific problem, if the problem uses units of hours or longer periods of time, it may be easier to calculate the velocity, then convert the final answer to meters/second.
Even in a scientific problem, if the problem uses units of hours or longer periods of time, it may be easier to calculate the velocity, then convert the final answer to meters/second.
Remember to include the direction (such as “forward” or “north”). In formula form, vav = Δs/Δt. The delta symbol Δ just means “change in,” so Δs/Δt means “change in position over change in time. " Average velocity can be written vav, or as a v with a horizontal line over it.
Remember to include the direction (such as “forward” or “north”). In formula form, vav = Δs/Δt. The delta symbol Δ just means “change in,” so Δs/Δt means “change in position over change in time. " Average velocity can be written vav, or as a v with a horizontal line over it.
Anna walks west at 1 m/s for 2 seconds, then instantly accelerates to 3 m/s and keeps walking west for 2 seconds. Her total displacement is (1 m/s west)(2 s) + (3 m/s west)(2 s) = 8 meters west. Her total time is 2s + 2s = 4s. Her average velocity is 8m west / 4s = 2 m/s west. Bart walks west at 5 m/s for 3 seconds, then turns around and walks east at 7 m/s for 1 second. We can treat the eastward movement as “negative movement west,” so total displacement = (5 m/s west)(3 s) + (-7 m/s west)(1 s) = 8 meters. Total time = 4s. Average velocity = 8 m west / 4s = 2 m/s west. Charlotte walks north 1 meter, then walks west 8 meters, then south 1 meter. It takes her 4 seconds total to walk this distance. Draw a diagram on a piece of paper, and you’ll see that she ends up 8 meters west of her starting point, so this is her displacement. Total time is 4 seconds again, so the average velocity is still 8 m west / 4s = 2 m/s west.
If the unit “m/s2” makes no sense to you, write it as “m/s/s” or “meters per second per second. “[6] X Research source An acceleration of 2 m/s/s means the velocity increases by 2 meters per second, each second.
At the beginning (time t = 0 seconds ), the bike is traveling right at 5 m/s. After 1 second (t = 1), the bike moves at 5 m/s + at = 5 m/s + (2 m/s2)(1 s) = 7 m/s. At t = 2, the bike is moving right at 5+(2)(2) = 9 m/s. At t = 3, the bike is moving right at 5+(2)(3) = 11 m/s. At t = 4, the bike is moving right at 5+(2)(4) = 13 m/s. At t = 5, the bike is moving right at 5+(2)(5) = 15 m/s.
Remember to include the direction, in this case “right. " These terms can instead be written as v0 (velocity at time 0, or initial velocity), and simply v (final velocity).
Remember to include the direction, in this case “right. " These terms can instead be written as v0 (velocity at time 0, or initial velocity), and simply v (final velocity).
Remember to include the direction, in this case “right. " These terms can instead be written as v0 (velocity at time 0, or initial velocity), and simply v (final velocity).
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+15)/2), ((7+13)/2), or ((9+11)/2) all equal 10 m/s right.
Since any one of these pairs average to the same amount, the average of all these velocities will be equal to this amount. In our example, the average of all of those “10 m/s right” will still be 10 m/s right. We can find this amount 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 be calculated using the formula above: (5+15)/2 = 10 m/s right.
s = vit + ½at2. (Technically Δs and Δt, or change in position and change in time, but you’ll be understood if you use s and t. ) Average velocity vav is defined as s/t, so let’s put the formula in terms of s/t. vav = s/t = vi + ½at Acceleration x time equals the total change in velocity, or vf - vi. So we can replace “at” in the formula and get: vav = vi + ½(vf - vi). Simplify: vav = vi + ½vf - ½vi = ½vi + ½vf = (vf + vi)/2.
