# Thread: Unknown time to work out speed

1. ## Unknown time to work out speed

Particle A has velocity (8i - 3j)ms^-1 and particle B has velocity (15i - 8j)ms^-1.

A) Find the speed of B
B)Find the velocity of B relative to A

2. A) Speed is just the magnitude of the velocity vector:

So, if particle B has velocity (15i - 8j) $\displaystyle ms^{-1}$, the speed is:

$\displaystyle v = \sqrt{15^2 - 8^2}$

$\displaystyle v = \sqrt{225 - 64}$

$\displaystyle v = \sqrt{161}$

$\displaystyle v = 12.7 ms^{-1}$

B) Relative velocity is just the difference of the velocities, so the velocity of B relative to A is:

$\displaystyle (15i - 8j) - (8i - 3j) = (7i - 5j) ms^{-1}$

3. thanks