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Grade 10Mechanics

The numerical value of ratio of instantaneous velocity to instantaneous speed is ?

Profile image of Harsh
9 Years agoGrade 10
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Profile image of SARAVANAN GANESAN
9 Years ago
Instantaneous speed at time "t" is defined as v = lim(x->0) delta(s)/ delta(t) = ds/dt, where delta(s) is the distance traveled in the time interval delta(t). Now, when we look at instantaneous velocity, it is defined as V = lim(x->0)delta(R)/delta (t) = dR/dt. I have written R and V in cap`s to indicate that they are vector quantities. Now, if the time interval is very very small, then delta(R) can be considered to be equal to delta(s). In that case the ratio of instantaneous speed and instantaneous velocity will be "ONE". In all other cases, their ratio will be ds/dR, where s = distance and R = is displacement of the particle.