Kinematics

JEE Main level, single correct, medium

139 of 308

Question 139 of 308

The co-ordinates of a moving particle at any time ' tt ' are given by x=αt3x=\alpha t^3 and y=βt3y=\beta t^3. The speed of the particle at time ' tt ' is given by

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Answer: (B) 3t2α2+β23 t^2 \sqrt{\alpha^2+\beta^2}

Vx=dxdt=3αt2,Vy=dydt=3βt2V_x=\frac{d x}{d t}=3 \alpha t^2, V_y=\frac{d y}{d t}=3 \beta t^2
v→=Vx2+Vy2=3t2α2+β2\overrightarrow{\mathrm{v}}=\sqrt{\mathrm{V}_{\mathrm{x}^2}+\mathrm{V}_{\mathrm{y}^2}}=3 \mathrm{t}^2 \sqrt{\alpha^2+\beta^2}

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