Question

Q1.The displacement of an object along the three axes are
given by, x = 2t', y=t" – 4t and z = 3t - 5. The initial
velocity of the particle is
(a) 10 units o n (b) 12 units
(C) 5 units
(a) 2 units​

Answer 1

Step-by-step explanation:

Given,

Displacement of an object along the three axes is

• x = 2t²
• y = t² - 4t
• z = 3t - 5

Relation between velocity (v) & displacement (s) is,

$\pink{ \boxed{ \blue{v = \frac{ds}{dt} }}}$

So,

$\begin{gathered}v_x = \frac{dx}{dt} \\ \\ v_x = \frac{d}{dt} (2t^2) = 4t \\ \\ \boxed{\therefore \: v_x = 4t \: \: \: \:} \: \: \\ \\ \: v_y = \frac{dy}{dt} \\ \\ v_y \: = \frac{d}{dt} ( {t}^{2} - 4t) \\ \\ v_y = 2t - 4\\ \\ \boxed{\therefore \: v_y = 2t - 4 \: \: \: \:} \\ \\ v_z = \frac{dz}{dt} \\ \\ \end{gathered}$

$</p><p>\begin{gathered}v_z = \frac{d}{dt} (3t - 5) \\ \\ v_z = 3 \\ \\ \boxed{\therefore \: v_z = 3 \: \: \: \:}\end{gathered}$

Initial velocity of the particle :

velocity of particle at t=0

$\begin{gathered}v _x = 4(0) \: \: =0 \\ v_y = 2(0) - 4 = - 4 \\ v_z = 3\end{gathered}$

Velocity of the particle is,

$\begin{gathered}V = \sqrt{ \: (v _x )^{2} + (v _y )^{2} +(v _z )^{2}} \\ \\ V = \sqrt{ {0}^{2} + {3}^{2} + {4}^{2} } \\ \\ V = \sqrt{25} =5 \end{gathered}$

Therefore, The initial velocity of the particle is 5 units.

Answer 2

Answer:

Michelangelo di Lodovico Buonarroti Simoni, known simply as Michelangelo, was an Italian sculptor, painter, architect and poet of the High Renaissance born in the Republic of Florence, who exerted an unparalleled influence on the development of Western art.