The co-ordinates of a moving particle at any time ' t ' are given by x = α t³ and y = β t³ where α and β are constants. The speed of the particle at time ' t ' is given by (a) t√(α² + β²) (b) 3t√(α² + β²) (c) t²√(α² + β²) (d) 3t²√(α² + β²)

Answer: (d). vx = 3α t², vy = 3β t² Speed = √(vx² + vy²) = 3t²√(α² + β²) So the answer is (d).

The co-ordinates of a moving particle at any time ' t ' are given by… | MHT CET 2024 (16 May, Shift 1)

Q10MHT CET 2024 · 16 MAY · SHIFT 1Medium

Velocity, Acceleration & Variable Motion

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

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Answer: (d)

$v_x = 3\alpha t^2$ , $v_y = 3\beta t^2$
Speed $= \sqrt{v_x^2 + v_y^2} = 3t^2\sqrt{\alpha^2 + \beta^2}$
So the answer is (d).

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