Question:
The co-ordinates of a moving particle at any time $'t'$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed to the particle at time $'t'$ is given by
The co-ordinates of a moving particle at any time $'t'$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed to the particle at time $'t'$ is given by
Updated On: Jul 2, 2022
- $3t\sqrt{\alpha^{2}+\beta^{2}}$
- $3t^2\sqrt{\alpha^{2}+\beta^{2}}$
- $t^2\sqrt{\alpha^{2}+\beta^{2}}$
- $\sqrt{\alpha^{2}+\beta^{2}}$
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The Correct Option is B
Solution and Explanation
Speed $=\left|\vec{v}\right|=\sqrt{\left(3\alpha t^{2}\right)^{2}+\left(3\beta t^{2}\right)^{2}}=3t^{2}\sqrt{\alpha^{2}+\beta^{2}}.$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration