Displacement, Time and Average Velocity
Displacement refers to the change in position of an object, while time measures the duration of an event. Average velocity is the displacement of an object divided by the time taken, indicating the overall rate of change in position. These concepts are fundamental in understanding the motion and behavior of objects in the field of physics.
3 Key excerpts on "Displacement, Time and Average Velocity"
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- W. Bolton(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...Chapter 4 Linear motion 4.1 Introduction This chapter is a review of the basic terms used in describing linear motion with a derivation of the equations used in tackling problems involving such motion. Also considered are the graphs of distance–time and velocity–time and the data that can be extracted from such graphs. The vector nature of velocity is c onsidered and its resolution into components, thus enabling problems to be tackled which involve projectiles. Chapter 5 extends this consideration of motion to that of angular motion. 4.1.1 Basic terms The following are basic terms used in the description of linear motion: Distance is the distance along the path of an object, whatever the form of the path. Thus, if we say the distance covered in the motion of a car was, say, 3 km then the 3 km could have been covered along a straight road and the car be 3 km away from its start point. Another possibility is, however, that the 3 km was round a circular track and the car at the end of its 3 km might have been back where it started. Displacement is the distance in a straight line between the start and end points of some motion. Thus a displacement of 3 km would mean that at the end of the motion that an object was 3 km away from the start point. Speed is the rate at which distance is covered. Thus a car might be stated as having a speed of 50 km/h. Average speed is the distance covered in a time interval divided by the time taken: A car which covers 80 km in 1 hour will have an average speed of 80 km/h over that time. 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...
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 +)...
