The co-ordinates of a moving particle at any time t are given by x = α t^3 and y = β t^3 . The speed of the particle at time t is given by: - Physics MCQ AIEEE 2003 2026 | ExamTest.live

mediumMCQAIEEE 20032026Physics

1 mark

The co-ordinates of a moving particle at any time t are given by x = α t^{3} and y = β t^{3} . The speed of the particle at time t is given by:

Solution & Step-by-step Explanation

The velocity components are: v_{x} = \frac{d x}{d t} = 3 α t^{2} v_{y} = \frac{d y}{d t} = 3 β t^{2} The speed v is the magnitude of the velocity vector: v = v_{x}^{2} + v_{y}^{2} = (3 α t^{2})^{2} + (3 β t^{2})^{2} v = 9 α^{2} t^{4} + 9 β^{2} t^{4} = 3 t^{2} α^{2} + β^{2}

Try it yourself before checking the explanation above.

The co-ordinates of a moving particle at any time t are given by x = α t^{3} and y = β t^{3} . The speed of the particle at time t is given by:

3 t^{2} α + β

3 t^{2} α^{2} + β^{2}

t^{2} α^{2} + β^{2}

α^{2} + β^{2}

Practice with timed mock tests and track your performance across Physics.