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Rectilinear Motion
Speed and Velocity
The speed of a particle is the distance it covers per unit time
regardless of any changes in the direction of motion. A particle
moves along the path from A to B and then from B to C covering the
whole distance in 1 second. Then the speed of the particle is 7metre/second.
Velocity is defined as rate of change of displacement.
The average velocity of a particle in a given time is the displacement
(straight line between initial and final positions) per unit time.
The velocity of the particle moving as above is not numerically
the same as its speed since there was a change in its direction
of motion. The net displacement is of 5 units from A to C. Since
this displacement occurred in 1second, the velocity is 5 metre/second.
Consider the two motions shown above. In both cases the starting
and ending positions coincide. Since there is change of direction
in each case, the speed differs in magniude from the velocity. Since
the initial and final positions are the same, there is no displacement.
Hence the velocity is zero in each case. The speed is given by the
actual distance covered divided by the time taken and is therefore
not zero.
For a particle moving in a straight line however, the speed and
velocity are the same in magnitude.
Displacement-Time Graphs
Shown below is a displacement-time graph for uniform motion i.e.
motion with constant velocity.
The slope gives the constant velocity
Given below in the figure are displacement time graphs of particles
A, B, C and D. The particle A has the same displacement at all times.
Hence it is stationary.
The particles B, C and D have different displacements at different
times. Hence these are all in motion.
In the displacement-time graphs for particles B and C the angle
() between the straight line and the x-axis is always the same.
Hence tan is always the same. But tan is also given by s/t which
is the velocity of the particle. Hence straight line graphs of displacement-time
indicate fixed velocity.
For particle D, the displacement-time graph indicates that in equal
times t, the displacements alter by different amounts. In the figure
above, the change in displacement s1 is smaller than the change
s2. Hence the velocity increases with ongoing time.
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