Acceleration
Acceleration is the rate of change of velocity over time. It can be positive (speeding up), negative (slowing down), or zero (constant speed). In physics, acceleration is a vector quantity, meaning it has both magnitude and direction, and is measured in units of distance per time squared (e.g., meters per second squared).
7 Key excerpts on "Acceleration"
eBook - ePub- Richard Gentle, Peter Edwards, William Bolton(Authors)
- 2001(Publication Date)
- Newnes(Publisher)
...We will see in the next section that this means that the driver will have to exert a force on the steering wheel which could be calculated. Often we take speed and velocity as the same thing and use the symbols v or u for both, but do not forget that there is a distinction. If the object is moving at a constant velocity v and it has travelled a distance of s in time t then the velocity is given by (4.1.1) Alternatively, if we know that the object has been travelling at a constant velocity v for a time of t then we can calculate the distance travelled as (4.1.2) Acceleration is the rate at which the velocity is changing with time and so it is defined as the change in velocity in a short time, divided by the short time itself. Therefore the units are metres per second (the units of velocity) divided by seconds and these are written as metres per second 2 (m/s 2). Acceleration is generally given the symbol a. Usually the term Acceleration is used for the rate at which an object’s speed is increasing, while deceleration is used when the speed is decreasing. Again, do not forget that a change in velocity could also be a directional change at a constant speed. Having defined some of the common quantities met in the study of kinematics, we can now look at the way that these quantities are linked mathematically. Velocity is the rate at which an object’s displacement is changing with time. Therefore if we were to plot a graph of the object’s displacement s against time t then the value of the slope of the line at any point would be the magnitude of the velocity (i.e. the speed). In Figure 4.1.1, an object is starting from the origin of the graph where its displacement is zero at time zero. The line of the graph is straight here, meaning that the displacement increases at a constant rate. In other words, the speed is constant to begin with and we could measure it by working out the slope of the straight line portion of the graph...
eBook - ePub- John Bird(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...Chapter 18 Acceleration Why it is important to understand: Acceleration Acceleration may be defined as a ‘change in velocity’. This change can be in the magnitude (speed) of the velocity or the direction of the velocity. In daily life we use Acceleration as a term for the speeding up of objects and decelerating for the slowing down of objects. If there is a change in the velocity, whether it is slowing down or speeding up, or changing its direction, we say that the object is accelerating. If an object is moving at constant speed in a circular motion – such as a satellite orbiting the earth – it is said to be accelerating because change in direction of motion means its velocity is changing even if speed may be constant. This is called centripetal (directed towards the centre) Acceleration. On the other hand, if the direction of motion of the object is not changing but its speed is, this is called tangential Acceleration. If the direction of Acceleration is in the same direction as that of velocity then the object is said to be speeding up or accelerating. If the Acceleration and velocity are in opposite directions then the object is said to be slowing down or decelerating. An example of constant Acceleration is the effect of the gravity of earth on an object in free fall. Measurement of the Acceleration of a vehicle enables an evaluation of the overall vehicle performance and response. Detection of rapid negative Acceleration of a vehicle is used to detect vehicle collision and deploy airbags. The measurement of Acceleration is also used to measure seismic activity, inclination and machine vibration...
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 - ePubInstant Notes in Sport and Exercise Biomechanics
Second Edition
- Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler(Authors)
- 2019(Publication Date)
- Garland Science(Publisher)
...Obviously, such knowledge of individual and comparative performances would have important training implications for both the athlete and the coach. Acceleration is defined as the change in velocity per unit of time and it is usually measured in metres per second squared (m/s 2). This means the velocity of an object will increase/decrease by an amount for every second of its motion. For example, a constant (uniform) Acceleration of 2.5 m/s 2 indicates that the body will increase its velocity by 2.5 m/s for every second of its motion (2.5 m/s for 1 second, 5.0 m/s for 2 seconds, 7.5 m/s for 3 seconds and so on). Table A1.3 shows the Microsoft Excel calculations that now include the Acceleration data for the 100 m sprint performance used in the previous example. Table A1.2 Microsoft Excel calculations (to two decimal places) of the velocity for each 10 m interval in the 100 m sprint data (d = displacement; dt = time for each 10 m; sum t = cumulative time; v = velocity; sd = standard deviation; max = maximum value; min = minimum value) Table A1.3 Microsoft Excel calculations (to two decimal places) of the Acceleration for each 10 m interval in the 100 m sprint (d = displacement; dt = time for each 10 m; sum t = cumulative time; v = velocity; a = Acceleration; sd = standard deviation; max = maximum value; min = minimum value) Acceleration can be represented by the...
eBook - ePubBiomechanics of Human Motion
Applications in the Martial Arts, Second Edition
- Emeric Arus, Ph.D.(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
...If we speak about an athlete who runs the distance of 1500 m, his speed varies during the time of running. At the very beginning, his speed is higher than during the remainder of the distance, which varies again depending on the tactical solutions of the athlete or depending on his endurance. At the end, his speed will increase again as he gets closer to the finish line. In martial arts, the speed has the utmost importance in any kind of technical execution; however, the factor of speed is negligible if the athlete has less force to sustain the speed and ultimately the Acceleration. In martial arts, the result of the speed and the force are the key factors for achieving victory. 6.3 Acceleration The Acceleration is the time rate of change of the velocity, which means that Acceleration tells us how fast the velocity is changing. An object can have a large velocity and zero Acceleration and vice versa. Whenever a body is acted upon by an unbalanced force, it will undergo Acceleration. If a body is moving in a constant straight direction, the force which is acting upon it will produce shortly a change in speed. The acting force may produce a change of speed and also a change of direction. In general, in order to produce Acceleration, a force must be applied to the body. According to Newton’s second law of motion (F = m · a), the magnitude of the force (F) must be directly proportional to both the mass (m) of the body and its Acceleration (a). Acceleration is measured by meters per second squared a = m/s 2. An explanation is important concerning why the Acceleration is measured as m/s 2. Taking the following mathematical expressions for average Acceleration, which states: a ¯ =∆ v /∆ t or a ¯ = (final m/s- initial m/s)/s, which becomes a ¯ = (m/s)/s. Acceleration can be positive or negative. An increase is considered positive, and a decrease in speed is considered negative...
eBook - ePub- J Jones, J Burdess, J Fawcett(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
...The derivative d x /d t is often written as, where the dot denotes differentiation with respect to time. Velocity, like position, is a vector quantity and in the case of straight line motion its direction is defined by its sign, which is the same as that of the incremental displacement δx. The recommended SI unit of time is the second, s, so that the SI unit of velocity will be m s −1. Acceleration If the point has velocity ν at time t, and time δt later has velocity ν + δv then the Acceleration a of the point is defined as its rate of change of velocity, i.e. The recommended SI unit of Acceleration is m s −2. Again the direction is defined by its sign and is positive if δv is positive. Thus, the Acceleration of the point is in the same direction as the incremental change in velocity, but not necessarily in the same direction as the displacement. For example, a positive displacement would give a positive velocity, but during the displacement the magnitude of the velocity could decrease. In this case δv would be negative, and the Acceleration would therefore be negative. This situation arises when applying the brakes in a vehicle. It is important to note that once we have defined the positive direction of the position x, we have also defined and positive in the same direction. In the above case x, and are all positive along OX. Given an expression for the position of a point as a function of time, i.e. x = f(t), it is now possible, using eqns (1.1) and (1.2), to calculate its velocity and Acceleration by successive differentiation of x with respect to time. Example 1.1 A point moves on a straight line with its position, measured from an origin O, given by x = A sin ωt...
eBook - ePub- A. D. Johnson(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...2.2 Displacement–time graph. v = s t so that t = s v t = 120000 208.33 = 576s or 9 min 36s 2.2.5 Acceleration When a car sets off from traffic lights the driver depresses the ‘accelerator’ and the car steadily increases velocity. In slowing the car the driver depresses the brake pedal, which can be considered as a ‘decelerator’ This example serves to define the terms Acceleration and deceleration; however, other descriptive terms for deceleration are retardation and negative Acceleration. Acceleration is the change in velocity compared to advancing time, or a = s t × 1 t = s t 2 where a = Acceleration in units of m/s 2. Example 2.2 The velocity of a car on a straight level road increases by 2.0 m/s every second as it accelerates from standstill until it reaches 40 m/s. Tabulate the velocity second by second. Solution The answer can be tabulated as follows: It can be seen that the Acceleration is uniform (constant) and as every second ticks by the velocity increases by 2 m/s. The Acceleration can, therefore, be seen to be 2 m/s 2. 2.2.6 Velocity–time graphs Acceleration can be defined as the rate of increase of velocity. It can be represented on a velocity–time graph as shown in Figure 2.3. Fig. 2.3 Velocity–time graph. The velocity–time graph is a progression from the displacement–time graph shown in Figure 2.2. Instead of displacement, velocity is measured on the vertical axis. When velocity is plotted against time, the graph line represents Acceleration. Figure 2.3 shows a straight graph line indicating uniform Acceleration; however, in practice, Acceleration can also vary. It should be noted that the area under the graph line represents displacement and can be calculated by determining areas directly from the graph but also by considering equation (2.1) : v = s t or, transposing, s = v × t...
