Average Velocity and Instantaneous Velocity
Average velocity is the total displacement of an object divided by the total time taken. It gives an overall picture of an object's motion. Instantaneous velocity, on the other hand, is the velocity of an object at a specific instant in time. It is determined by calculating the slope of the tangent to the position-time graph at that instant.
4 Key excerpts on "Average Velocity and Instantaneous Velocity"
eBook - ePub- Alan Hendrickson(Author)
- 2012(Publication Date)
- Routledge(Publisher)
...Because of the finite time interval of Δ t, the position of the object at any point in time between t 1 and t 2 is not known. The object may have been constantly oscillating back and forth during Δ t and only happened to be in the same place when position measurements were taken. Formula 1.2 gives us only the average velocity. If the time interval Δ t were made very small, then it is more likely that any movement of the object would be caught during Δ t and as a result reflected in v. The time interval Δ t cannot be made zero because division by zero is not allowed. However through the mathematics of calculus Δ t can become infinitesimally small. This book requires no use of calculus mainly because the movements we analyze are simple, and our needs are for quickly obtained reasonably close estimates of powers and forces. The formulas below for instantaneous velocity and acceleration are given because they provide completeness, and for those who do understand them and may find them illuminating, they may be skipped over without harm. When the change in time does become infinitesimally small the resultant velocity figure obtained is the true velocity at that instant in time, called instantaneous velocity. Mathematically: v = l i m Δ t → 0 Δ x Δ t = d x d t If the speed and direction of movement of an object is constant, then average and instantaneous velocities are equal: v ¯ = v = Δ x Δ t = d x d t t r u e o n l y i f v e l o c i t y i s c o n s t a n t Velocity is a displacement per unit of time, and so the units used in theatre are typically feet per second, feet per minute, and meters per second. Outside of theatre, miles per hour, kilometers per hour, and furlongs per fortnight are common. EXAMPLE: A drop flies in a distance of 40 feet in 8 seconds. What is its average velocity? SOLUTION: A direction convention must first be assumed, so pick “in” as + (a completely arbitrary choice, “out” could have been called +)...
eBook - ePub- W. Bolton(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...During the hour it may, however, have gone faster than 80 km/h for part of the time and slower than that for some other part. 5 A constant or uniform speed occurs when equal distances are covered in equal intervals of time, however small a time interval we consider. Thus a car with an average speed of 60 km/h for 1 hour will be covering distance at the rate of 60 km/h in the first minute, the second minute, over the first quarter of an hour, over the second half hour, indeed over any time interval in that hour. 6 Velocity is the rate at which displacement along a straight line changes with time. Thus an object having a velocity of 5 m/s means that the object moves along a straight line path at the rate of 5 m/s. 7 Average velocity is the displacement along a straight line occurring in a time interval divided by that time: Thus an object having a displacement of 3 m along a straight line in a time of 2 s will have an average velocity in the direction of the straight line of 1.5 m/s over that time. During the 2 s there may be times when the object is moving faster or slower than 1.5 m/s. 8 A constant or uniform velocity occurs when equal displacements occur in the same straight line direction in equal intervals of time, however small the time interval. Thus an object with a constant velocity of 5 m/s in a particular direction for a time of 30 s will cover 5 m in the specified direction in each second of its motion. 9 Acceleration is the rate of change of velocity with time. The term retardation is often used to describe a negative acceleration, i.e. when the object is slowing down rather than increasing in velocity. 10 Average acceleration is the change of velocity occurring over a time interval divided by the time: Thus if the velocity changes from 2 m/s to 5 m/s in 10 s then the average acceleration over that time is (5 - 2)/10 5 0.3 m/s 2. If the velocity changes from 5 m/s to 2 m/s in 10 s then the average acceleration over that time is (22 5)/10 5 20.3 m/s 2, i.e...
eBook - ePub- A. D. Johnson(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...2.1 Displacement diagram. Figure 2.1 gives an example of a man who walks 3 km east then 4 km north. He has actually walked a distance of 7 km but has been displaced from his start point by only 5 km. 2.2.2 Velocity Velocity is the value of displacement measured over a period of time. It is the rate over which a distance/displacement is traversed. The magnitude of velocity is often expressed in convenient units such as kilometres per hour or miles per hour; however, these should be regarded as observation and comparison units. For analysis purposes velocity is better expressed in SI units of m/s. 2.2.3 Average velocity Consider a car travelling between two towns at an average velocity of 50 km/h. On the journey the car will have stopped at traffic lights, crawled in traffic queues and ‘speeded up’ on fast stretches of road. It would be difficult to record the variations in velocity throughout the journey but average velocity can be considered as follows: average velocity = total distance total time taken say 75.km 15h = 50km/h The average velocity ignores the variations in the actual velocity and gives a value which assumes the whole journey to have been undertaken at a constant velocity of 50 km/h. An example of an average velocity calculation is when ‘lap time’ is recorded for a racing car completing laps on a racing circuit. The lap time is taken from the start of the lap to the completion of the lap and can then be used to calculate the average velocity using the known distance around the circuit. Constant velocity is a special value because it assumes that a body moves over equal distances in equal intervals of time. In terms of the car considered above, it would need to start instantly, move in a given direction at 50 km/h and continue at that velocity, without variation, until it reached its destination, where it would instantly stop. This situation is obviously not practical but for analysis it is sometimes useful to consider...
eBook - ePub- Rajpal S. Sirohi(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...11 Measurement of Velocity 11.1 INTRODUCTION Velocity is defined as the rate of change of position vector. It thus requires the measurement of positions at two time intervals; this would yield the average velocity. If the time interval is exceedingly small, we obtain instantaneous velocity. Measurement of velocity is required in several areas; notable of these are fluid mechanics and aerodynamics. We do require measurement of blood flow in biomedicine. It is known that the frequency of light reflected from a moving object is Doppler shifted and the Doppler shift is directly proportional to the velocity. The application of this fact for measuring velocity became possible only after the advent of laser. Several other velocity-measuring techniques were also developed later. Almost all the optical techniques of velocity measurement require a transparent or nearly transparent fluid, which is seeded with particles. They rely for their operation on the detection of scattered light from these seeded particles. These techniques fall in the domain of laser anemometry. These techniques really do not measure the velocity of the fluid but rather of the particles (scatterers). Therefore, the scatterers are assumed to follow the fluid flow faithfully. The particle density of scatterers should not be less than 10 10 particles/m 3. The particle size for measuring the gas flow ranges from 1 to 5 μm and for measuring the liquid flow say of water from 2 to 10 μm. Laser anemometry offers several advantages over hot-wire anemometry. These include noncontact measurement avoiding any interference to the flow, excellent spatial resolution, fast response and hence fluctuating velocities can be measured, no transfer function as the output voltage is linearly related to velocity, large measurement range, and can be used to measure both the liquid and the gas flows. It also has the advantage to be used both in forward- and backward-scattering directions...
