what does |dv/dt| and d|v|/dt represent . Can these be equal.

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Solution

d|v| /dt means the rate of change of magnitude of velocity with respect to time. On the other hand |dv/dt| means the magnitude of rate of change in velocity with respect to time (i.e. the magnitude of acceleration).
Lets take an example:
A body was travelling at 5m/s along the positive x-axis. Its velocity changed to 3m/s along negative x- axis in 1 second.
Here ,
d|v|/dt = (3 - 5)/1
= -2m/s^2

|dv/dt| = (-3 - 5)/1
= -8m/s^2
Hence these both cannot be equal.

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∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ a n d \frac{d | \to v |}{d t}

d ϕ = f (T) d T + (T / V) d V a n d d ψ = T d p + (T / p^{2}) d V,

\to v \cdot \to a / v,

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\frac{d v}{d t}

v

t = t_{0}

v = 0

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\frac{d v}{d t} = 0

\frac{d^{2} v}{d t^{2}} =

\frac{d | \to v |}{d t} = 0 w h i l e ∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ \neq 0

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