Question

Velocity of a particle at some instant is v=(3hat i + 4hat j + 5hat k) m//s. Find speed of the particle at this instant.

Answer 1

The speed of particle is 5√2

Step by step explanation:

Speed is a scaler quantity , The distance covered per unit time is called speed.

Velocity is a vector quantity, which is also known as speed with direction.

$\textbf{\Large Speed is the magnitude of velocity vector.}$

To find the magnitude of vector (x i  +y j +z k )

magnitude =$\sqrt{(x)^2 + (y)^2 + (z)^2 }$                           (equation 1)

In this case     velocity  $\textbf{\Large v = 3i + 4j +5k}$

So,    x= 3,  y = 4, z = 5  

Putting the values in equation 1,

Speed =

$\sqrt{(3)^2 + (4)^2 + (5)^2} = \sqrt {9 + 16 + 25} = \sqrt {50} =\sqrt{25\times 2}\\\\\textbf{\Large So the speed of particle = }5\sqrt {2} \frac{m}{s}$