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The co-ordinates of a moving particle at any time 't' are given by x = αt³ and y = βt³. The speed of the particle at time 't' is given by

1. 3t√(α² + β²)
2. 3t²√(α² + β²)
3. t²√(α² + β²)
4. √(α² + β²)

Correct answer: 3t²√(α² + β²)

Solution

The speed of the particle is derived from the derivatives of its position coordinates with respect to time. By differentiating x and y with respect to t, we find the velocity components, and using the Pythagorean theorem to combine them gives the speed as 3t²√(α² + β²).

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