Расчет как найти скорость

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   Set up an equation with position and time instead. You can also find the velocity from the object’s change in position and time. This works for any problem. Note that, unless the object is moving at a constant velocity, your answer will be the average velocity during the movement, not the specific velocity at a certain time.^[4]
   

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   Find the distance between the start and end points. When measuring velocity, the only positions that matter are where the object started, and where the object ended up. This, along with which direction the object traveled, tells you the displacement, or change in position.^[5]
   The path the object took between these two points does not matter.

   • Example 1: A car traveling due east starts at position x = 5 meters. After 8 seconds, the car is at position x = 41 meters. What was the car’s displacement?
     • The car was displaced by (41m – 5m) = 36 meters east.
   • Example 2: A diver leaps 1 meter straight up off a diving board, then falls downward for 5 meters before hitting the water. What is the diver’s displacement?
     • The diver ended up 4 meters below the starting point, so her displacement is 4 meters downward, or -4 meters. (0 + 1 – 5 = -4). Even though the diver traveled six meters (one up, then five down), what matters is that the end point is four meters below the start point.

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   Calculate the change in time. How long did the object take to reach the end point? Many problems will tell you this directly. If it does not, subtract the start time from the end time to find out.^[6]
   

   • Example 1 (cont.): The problem tells us that the car took 8 seconds to go from the start point to the end point, so this is the change in time.
   • Example 2 (cont.): If the diver jumped at t = 7 seconds and hits the water at t = 8 seconds, the change in time = 8s – 7s = 1 second.

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   Divide the total displacement by the total time. In order to find the velocity of the moving object, you will need to divide the change in position by the change in time. Specify the direction moved, and you have the average velocity.^[7]
   

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   Solve problems in two dimensions. Not all word problems involve movement back along one line. If the object turns at some point, you may need to draw a diagram and solve a geometry problem to find the distance.

   • Example 3: A man jogs for 3 meters east, then make a 90º turn and travels 4 meters north. What is his displacement?
     • Draw a diagram and connect the start point and end point with a straight line. This is the hypotenuse of a triangle, so solve for its length of this line using properties of right triangles. In this case, the displacement is 5 meters northeast.
     • At some point, your math teacher may require you to find the exact direction traveled (the angle above the horizontal). You can do this by using geometry or by adding vectors.

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   Understand the velocity formula for an accelerating object. Acceleration is the change in velocity. If the acceleration is constant, the velocity continues to change at the same rate.^[8]
   We can describe this by multiplying acceleration and time, and adding the result to the initial velocity:

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   Multiply the acceleration by the change in time. This will tell you how much the velocity increased (or decreased) over this time period.^[9]
   

   • Example: A ship sailing north at 2 m/s accelerates north at a rate of 10 m/s². How much did the ship’s velocity increase in the next 5 seconds?
     • a = 10 m/s²
     • t = 5 s
     • (a * t) = (10 m/s² * 5 s) = 50 m/s increase in velocity.

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   Add the initial velocity. Now you know the total change in the velocity. Add this to the initial velocity of the object, and you have your answer.^[10]
   

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   Specify the direction of movement. Unlike speed, velocity always includes the direction of movement. Make sure to include this in your answer.

   • In our example, since the ship started going north and did not change direction, its final velocity is 52 m/s north.

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   Solve related problems. As long as you know the acceleration, and the velocity at any one point in time, you can use this formula to find the velocity at any other time. Here’s an example solving for the initial velocity:

   • “A train accelerates at 7 m/s² for 4 seconds, and ends up traveling forward at a velocity of 35 m/s. What was its initial velocity?”

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   Learn the formula for circular velocity. Circular velocity refers to the velocity that one object must travel in order to maintain its circular orbit around another object, usually a planet or other gravitating mass.^[11]
   

   • The circular velocity of an object is calculated by dividing the circumference of the circular path by the time period over which the object travels.
   • When written as a formula, the equation is:
     • v = ^(2πr) / _T
   • Note that 2πr equals the circumference of the circular path.
   • r stands for “radius”
   • T stands for “time period”

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   Multiply the circular radius by 2π. The first stage of the problem is calculating the circumference. To do this, multiply the radius by 2π. If you are calculating this by hand, you can use 3.14 as an approximation for π.^[12]
   

   • Example: Find the circular velocity of an object traveling a circular path with a radius of 8 m over a full time interval of 45 seconds.
     • r = 8 m
     • T = 45 s
     • Circumference = 2πr = ~ (2)(3.14)(8 m) = 50.24 m

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   Divide this product by the time period. In order to find the circular velocity of the object in question, you need to divide the calculated circumference by the time period over which the object traveled.^[13]
   

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

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Calculator, Practice Problems, and Answers

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• Meters per second (m/s) is the standard scientific unit for velocity.^[14]
  Make sure your units match by measuring distance in meters (m), time in seconds (s), and acceleration in meters per second per second (m/s²).^[15]
  

• Average velocity measures the average velocity an object travels over the full course of its path. Instantaneous velocity measures the velocity of an object at a specific moment along its path.

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