Question

The position vector of a particle is given
F = 2t î+3t(square) j^ - 5 k^
a) Calculate the velocity and speed of the
particle at any instant t.
b) Calculate the velocity and speed of the
particle at time t=2's

Solution

The velocity v = dr/dt = 2i^+6tj^
The speed v(t)= √2^2+√(6t)^2 ms-1

any one pls tell me how does velocity and speed found
step by step definition pls​

Answer 1

Explanation:

the difference between speed and velocity is

the velocity has direction while speed does not

so

a)

velocity of the given position vector is

dF/dt = 2i + 6t j

and speed is √(4 + 36t²)

b) velocity at time 2s is

v = 2i + 12j

v = √(4 + 144) = √148

direction is tan∅ = 12/2 = 6

∅ = tan^-1 (6)

and speed is

√(4 + 144) = √148