At an instant t, the coordinate of a particles are x=at2,y=bt2 and z=0. The magnitude of velocity of particle at an instant t is

Question

At an instant t, the coordinate of a particles are x=at2,y=bt2 and z=0. The magnitude of velocity of particle at an instant t is (A)  t√a2+b2  (B)  (v/√2)  (C)  (v/√3)  (D)  2t√a2+b2

Tardigrade Admin · Accepted Answer

Here, displacement at an instant? Is s=at2 hati+bt2 hatj v=(ds/dt)=2at hati+2bt hatj |v|=√(2at)2+(2bt)2 =2t√a2+b2

Q. At an instant t, the coordinate of a particles are $x = a t^{2}, y = b t^{2}$ and $z = 0.$ The magnitude of velocity of particle at an instant t is

$t a^{2} + b^{2}$

$\frac{v}{2}$

$\frac{v}{3}$

$2 t a^{2} + b^{2}$

Here, displacement at an instant? Is $s = a t^{2} \hat{i} + b t^{2} \hat{j}$ $v = \frac{d s}{d t} = 2 a t \hat{i} + 2 b t \hat{j}$ $∣ v ∣ = (2 a t)^{2} + (2 b t)^{2}$ $= 2 t a^{2} + b^{2}$

Q. At an instant t, the coordinate of a particles are x=at2,y=bt2 and z=0. The magnitude of velocity of particle at an instant t is

ta2+b2​

2​v​

3​v​

2ta2+b2​