Average Velocity and Acceleration
Average velocity is the displacement of an object over a specific time interval, while average acceleration is the change in velocity over the same time interval. Velocity is a vector quantity, meaning it has both magnitude and direction, while acceleration measures the rate of change of velocity. Both are important concepts in understanding the motion of objects in physics.
6 Key excerpts on "Average Velocity and Acceleration"
eBook - ePubInstant Notes in Sport and Exercise Biomechanics
Second Edition
- Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler(Authors)
- 2019(Publication Date)
- Garland Science(Publisher)
...The biomechanical study of human motion requires an understanding of the precise relationship between the changes in these variables. As outlined elsewhere in this text, it is shown that the average velocity of any moving object is given by the change in position (displacement) divided by the time over which the change takes place. If position is represented by the letter p and time by the letter t, the average velocity (v) between time 1 and time 2 may be determined using: v = p 2 − p 1 t 2 − t 1 o r Δ p Δ t The capital Greek letter delta (Δ) is used to denote the change in a variable. The average velocity is also called the rate of change of displacement. Remember, velocity is a vector quantity and therefore this represents the average velocity in a specific direction; if the direction is not specified or is unimportant to the situation then the above equation is preferably termed the average speed. Similarly, the average acceleration (a), or rate of change of velocity, between time 1 and time 2 may be determined from the equation: a = v 2 - v 1 t 2 - t 1 o r Δ v Δ t Returning to the calculation of velocity, Figure A4.1a graphically represents the change in position (displacement) of a moving object plotted against time. From this it can be seen that the equation for the average velocity between p 1 and p 2 is, in fact, the same equation that gives the slope or gradient of the line between the points marked A and B, which correspond to the times t 1 and t 2, respectively. Similarly, the gradient of the line between points C and D must be the average velocity of the object over the smaller time interval (δ t). The Greek lower-case letter delta (δ) is used here to denote a small change in some quantity, in this case a small change in time...
eBook - ePub- Alan Hendrickson(Author)
- 2012(Publication Date)
- Routledge(Publisher)
...The rate at which velocity changes with time is important too, and this is called acceleration. Average acceleration is defined as: a ¯ = Δ v Δ t Where a ¯ = average acceleration (ft/sec 2, m/sec 2) v = velocity (ft/sec, m/sec) t = time (seconds) Using the same logic as was used earlier in the discussion on velocity, because the finite time interval Δ t is involved, this is an average acceleration. Instantaneous acceleration will be obtained only if Δ t is infinitesimally larger than zero. a = l i m Δ t → 0 Δ v Δ t = d v d t If there is no change in velocity, meaning that velocity is constant, or stated mathematically Δ v = 0, then a = 0. Acceleration is the ratio of velocity change to time. The units of acceleration are therefore the units of velocity divided by the unit of time. This is expressed one of two ways, displacement per time per time, or displacement per time squared. Commonly this would be stated as “feet per second per second” or “feet per second squared”, and written as ft/sec/sec or ft/sec 2 (or likewise m/sec/sec, or m/sec 2). The rate at which acceleration changes with respect to time is somewhat amusingly called jerk. This quantity is rarely used but deserves mention because its presence is very perceptible. Jerky motion can result from elastic or springy elements within a mechanical system. Any blockage of movement is temporarily allowed by the springy element, but eventually forces build up and overcome the blockage and the springs stored force is released, causing the load to surge ahead...
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 - ePubAutomotive Accident Reconstruction
Practices and Principles, Second Edition
- Donald E. Struble, John D. Struble(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
...Therefore what-if questions may focus on the effects of varying the perception–reaction time from say a ½ to 2½ sec. Constant Acceleration The simplest kind of motion is at constant velocity, for which “rest” is simply a special case. Most often, though, time–distance studies involve vehicles that are being accelerated. The type of acceleration that is simplest to analyze is a constant, for which constant velocity (zero acceleration) is a special case. If a trajectory can be divided into segments with constant acceleration (as has been done in Chapters 3 and 4), the resulting analysis will cover the vast majority of questions asked of the reconstructionist. Generally, it is not necessary to make the segments small, but of course the velocity and the travel distance need to be continuous functions over an entire path. It is possible to write a general-purpose computer program in which different formulas are used in various segments, depending on what is known and what is unknown in any given segment. One can even do a forward-directed or a backward-directed calculation, depending on whether the velocity at the end is known (a final-value problem) or the velocity at the beginning is known (an initial-value problem). Obviously, a lot of IF-THEN-ELSE constructs must be employed. In all cases, the object is to wind up knowing the velocity at each of the segment boundaries, otherwise known as the key points. In addition, the user should have access to both the elapsed time (which is a forward measure) and the remaining time (which is a backward measure). Often the final event is a collision, though it could also be a vehicle coming to rest or even something else. Similarly, the user should know or be able to calculate the elapsed distance and the remaining distance. In each segment, the user should know or be able to calculate Δ S, the segment length, and Δ t, the segment time. The time–distance study can (and usually does) involve more than one vehicle...
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...
