..... Click the link for more information. of a body with respect to time. Since velocity is a vector U [−3,1] and V [5,2], one can add their corresponding components to find the resultant vector R [2,3], or one can graph U and V on a set of coordinate axes and complete the parallelogram formed with U and V
..... Click the link for more information. quantity, involving both magnitude and direction, acceleration is also a vector. In order to produce an acceleration, a force force, commonly, a "push" or "pull," more properly defined in physics as a quantity that changes the motion, size, or shape of a body. Force is a vector quantity, having both magnitude and direction.
..... Click the link for more information. must be applied to the body. The magnitude of the force F must be directly proportional to both the mass of the body m and the desired acceleration a, according to Newton's second law of motion, F=ma. The exact nature of the acceleration produced depends on the relative directions of the original velocity and the force. A force acting in the same direction as the velocity changes only the speed speed, change in distance with respect to time. Speed is a scalar rather than a vector quantity; i.e., the speed of a body tells one how fast the body is moving but not the direction of the motion.
..... Click the link for more information. of the body. An appropriate force acting always at right angles to the velocity changes the direction of the velocity but not the speed. An example of such an accelerating force is the gravitational force exerted by a planet on a satellite moving in a circular orbit. A force may also act in the opposite direction from the original velocity. In this case the speed of the body is decreased. Such an acceleration is often referred to as a deceleration. If the acceleration is constant, as for a body falling near the earth, the following formulas may be used to compute the acceleration a of a body from knowledge of the elapsed time t, the distance s through which the body moves in that time, the initial velocity vi, and the final velocity vf:
a=(vf2−vi2)/2s
a=2(s−vit)/t2
a=(vf−vi)/t
acceleration
Rate of change of velocity. Acceleration, like velocity, is a vector quantity: it has both magnitude and direction. The velocity of an object moving on a straight path can change in magnitude only, so its acceleration is the rate of change of its speed. On a curved path, the velocity may or may not change in magnitude, but it will always change in direction, which means that the acceleration of an object moving on a curved path can never be zero. If velocity is stated in metres per second (m/s) and the time interval in seconds (s), then the units of acceleration are metres per second per second (m/s/s, or m/s2). See also centripetal acceleration.
acceleration
See accelerator.
acceleration
acceleration [ak‚sel·ə′rā·shən]
Acceleration
The time rate of change of velocity. Since velocity is a directed or vector quantity involving both magnitude and direction, a velocity may change by a change of magnitude (speed) or by a change of direction or both. It follows that acceleration is also a directed, or vector, quantity. If the magnitude of the velocity of a body changes from v1 ft/s to v2 ft/s in t seconds, then the average acceleration a has a magnitude given by Eq. (1):
Instantaneous acceleration is defined as the limit of the ratio of the velocity change to the elapsed time as the time interval approaches zero. When the acceleration is constant, the average acceleration and the instantaneous acceleration are equal.
Whenever a body is acted upon by an unbalanced force, it will undergo acceleration. If it is moving in a constant direction, the acting force will produce a continuous change in speed. If it is moving with a constant speed, the acting force will produce an acceleration consisting of a continuous change of direction. In the general case, the acting force may produce both a change of speed and a change of direction.
Angular acceleration is a vector quantity representing the rate of change of angular velocity of a body experiencing rotational motion. If, for example, at an instant t1, a rigid body is rotating about an axis with an angular velocity ω1, and at a later time t2, it has an angular velocity ω2, the average angular acceleration α is given by Eq. (2),
When a body moves in a circular path with constant linear speed at each point in its path, it is also being constantly accelerated toward the center of the circle under the action of the force required to constrain it to move in its circular path. This acceleration toward the center of path is called radial acceleration. The component of linear acceleration tangent to the path of a particle subject to an angular acceleration about the axis of rotation is called tangential acceleration. See Rotational motion
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