A particle has initial velocity \((2i ⃗+3j ⃗)\) and acceleration \((0.3i ⃗+0.2j ⃗ ).\) The magnitude of velocity after 10 seconds will be

CONCEPT:

Velocity:

• The rate of change of displacement of a body is called the velocity of that body.
• It is a vector quantity that has both magnitudes as well as direction. 

\({\rm{Velocity\;}}\left( {\rm{V}} \right) = \frac{{Change\;in\;displacement}}{{Time\;taken}} = \frac{{{S_2} - {S_1}}}{{{t_2} - {t_1}}}\)

Where S2 is the final displacement at time t2 and S1 is the initial displacement at time t1.

Acceleration: 

• The rate of change of velocity is called an acceleration of the body.
• It is a vector quantity that has both magnitudes as well as direction.

\(a = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}\)

Where v2 = Final velocity and v1 = Initial velocity of an object at the time respectively

• The relationship between velocity and acceleration in an equation of motion is given by 

V = U + at

Where V= final velocity, a = acceleration, U = Intial Velocity, t =time

CALCULATION:

Given - \(v=(2i ⃗+3j ⃗)\) ,  \(a=(0.3i ⃗+0.2j ⃗ )\)

From laws od motion,

⇒ v = u + at

\(\Rightarrow v=(2i ⃗+3j ⃗)+ (0.3i ⃗+0.2j ⃗ )\times 10\)

\(\Rightarrow V=5i ⃗+5j ⃗\)

\(\Rightarrow \left | V \right |=\sqrt{5^{2}+5^{2}}\)

\(\Rightarrow V = 5\sqrt{2} ms^{-1}\)