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

Dario Meza

Dario Meza

Answered question

2022-12-01

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

Answer & Explanation

crys07bhZ

crys07bhZ

Beginner2022-12-02Added 8 answers

d|v| /dt refers to the rate at which the magnitude of velocity varies with respect to time. On the other hand, |dv/dt| denotes the rate of change in velocity with respect to time in terms of magnitude (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 | / d t = ( 3 5 ) / 1
= 2 m / s 2
| d v / d t | = ( 3 5 ) / 1
= 8 m / s 2
As a result, these two cannot be equal.

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