The coordinates of a moving particle at any time t are given by x=α t3 and y=t3. The speed of the particle at time t is given by

Question

The coordinates of a moving particle at any time t are given by x=α t3 and y=t3. The speed of the particle at time t is given by (A)  3t√α 2+β 2  (B)  3t2√α 2+β 2  (C)  t2√α 2+β 2  (D)  √α 2+β 2

Tardigrade Admin · Accepted Answer

x=α t3, y=β t3 vx=(dx/dt)=3α t2 vy=(dy/dt)=3β t2 Resultant velocity, v=√vx2+vy2 =√9α 2t4+9β 2t4 =3t2√α 2+β 2

Q. The coordinates of a moving particle at any time t are given by $x = α t^{3}$ and $y = t^{3} .$ The speed of the particle at time t is given by

$3 t α^{2} + β^{2}$

$3 t^{2} α^{2} + β^{2}$

$t^{2} α^{2} + β^{2}$

$α^{2} + β^{2}$

$x = α t^{3}, y = β t^{3}$ $v_{x} = \frac{d x}{d t} = 3 α t^{2}$ $v_{y} = \frac{d y}{d t} = 3 β t^{2}$ Resultant velocity, $v = v_{x}^{2} + v_{y}^{2}$ $= 9 α^{2} t^{4} + 9 β^{2} t^{4}$ $= 3 t^{2} α^{2} + β^{2}$

Q. The coordinates of a moving particle at any time t are given by x=αt3 and y=t3. The speed of the particle at time t is given by

3tα2+β2​

3t2α2+β2​

t2α2+β2​

α2+β2​