expression for velocity vector in 2d
Answers
For motion in two dimensions, the earlier kinematics equations must be expressed in vector form. For example, the average velocity vector is v = ( d f − d o )/ t, where d o and d f are the initial and final displacement vectors and t is the time elapsed.
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Answer:
expression for vector in two dimensions
Explanation:
For motion in two dimensions, the earlier kinematics equations must be expressed in vector form. For example, the average velocity vector is v = ( d f − d o )/ t, where d o and d f are the initial and final displacement vectors and t is the time elapsed. As noted earlier, the velocity and displacement vectors are shown in bold type, whereas the scalar (t) is not. In similar fashion, the average acceleration vector is a = ( v f − v o )/ t, where v o and v f are the initial and final velocity vectors.
An important point is that the acceleration can arise from a change in the magnitude of the velocity (speed) as well as from a change in the direction of the velocity. If an object travels around a circle at a constant speed, there is an acceleration due to the change in the direction of the velocity, even though the magnitude of the velocity does not change. A mass moves in a horizontal circle with a constant speed in Figure . The velocity vectors at positions 1 and 2 are subtracted to find the average acceleration, which is directed toward the center of the circle. (Note that the average acceleration vector is placed at the midpoint of the path in the given time interval.)
image is attached
Figure 6
Velocity and acceleration vectors of an object moving in a circle
The following discussion summarizes the four different cases for acceleration in a plane:
Case 1: Zero acceleration
Case 2: Acceleration due to changing direction but not speed
Case 3: Acceleration due to changing speed but not direction
Case 4: Acceleration due to changing both speed and direction.
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