Why instantaneous speed and instantaneous velocity equal?
Answers
#BAL
Instantaneous velocity is not the same as speed ( velocity is vector quantity but speed is a scalar quantity so how can a vector quantity be equal to scalar quantity??.)
Magnitude of instantaneous velocity is equal to speed.
Assume a particle moving on a curved path. Let the instantaneous velocity magnitude is given by V and speed is given by v.
Magnitude of velocity=dr/dt
Where dr is the displacement in time dt.
Speed = ds/dt
Where ds is the distance covered in time dt.
Now
magnitude of dr=ds
Therefore
magnitude of inst. velocity =speed.
The reasons for this are
For time interval dt there may be acceleration but in such a small time there cannot be an appreciable change in the velocity/ speed. So we assume for such a small interval V (velocity)and v(speed) are constant.
Also the path may be curved to the largest possible extent but in a small interval dt the magnitude of displacement vector dr and distance covered ds must be same.
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Instantaneous velocity. The rate of change of displacement of an object in a particular direction is its velocity.The magnitude of instantaneous velocity equals the instantaneous speed. This happens because, for an infinitesimally small time interval, the motion of a particle can be approximated to be uniform.