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The (x, y, z) coordinates of two points A and B are given respectively as (0, 4, 2) and (2, 8, 4). The displacement vector from A to B is:
Displacement vector from A to B is given by
A person moves 30 m north, then 30 m east, then 30√2 m southwest. His displacement from the original position is:
Resolving displacement 30√2 m southwest into two rectangular components, we get
Displacement in south
∴ Effective displacement due to 30 m north and 30 m south is zero.
Also effective displacement due to 30 m east and 30 m west in zero.
A bird flies from (3m, 4m, 3m) to (7m, 2m, 3m) in the xyz coordinates. The bird's displacement vector is given by
On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, the displacement of the motorist at the third turn is
The path followed by the motorist is a regular hexagon ABCDEF of side 500 m, as shown in the given figure. Let the motorist starts from A and takes the third turn at D.
Therefore, the magnitude of this displacement is
AD = AG + GD = 500 m + 500 m = 1000 m
Four girls skating on circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in figure. For which girl displacement is equal to the actual length of path?
Displacement of each girl =
Magnitude of displacement for each girl
For girl C, displacement = actual length of path.
A particle starts moving from point (2, 10, 1). Displacement for the particle is The final coordinates of the particle is
Initial position vector of the particle,
Let final position vector of the particle be
Hence, the final coordinates of the particle are ((10, 8, 2)
For any arbitrary motion in space, which of the following relations is true?
The relation (b) is true, others are false because relations (a), (c) and (d) hold only for uniformly accelerated motion.
The position of a particle is given by where t is in seconds and the coefficients have the proper units forto be in metres. The direction of velocity of the particle at t = 1 s is
Let θ be angle which the direction ofmakes with the
From the previous question,
Acceleration of the particle remains constant at all times.
If x = 5t + 3t^{2} andy = 4t are the x and y coordinates of a particle at any time t second where x and y are in metre, then the acceleration of the particle
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