Question:
A particle has initial velocity $ ( 2 \vec{i} + 3 \vec{j})$ and acceleartion ($ 0 . 3 \vec{i} + 0 . 2 \vec{j})$ The magnitude of velocity after 10 seconds will be
A particle has initial velocity $ ( 2 \vec{i} + 3 \vec{j})$ and acceleartion ($ 0 . 3 \vec{i} + 0 . 2 \vec{j})$ The magnitude of velocity after 10 seconds will be
Updated On: May 4, 2024
- 9 $ \sqrt 2 $ units
- 5 $ \sqrt 2 $ units
- 5 units
- 9 units
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The Correct Option is B
Solution and Explanation
$\vec{ v }=\overrightarrow{ u }+\vec{ a } t$
$\vec{ v }=(2 \hat{ i }+3 \hat{ j })+(0.3 \hat{ i }+0.2 \hat{ j }) \times 10$
$\Rightarrow \vec{ v }=5 \hat{ i }+5 \hat{ j }$
$v =5 \sqrt{2}$ units
$\vec{ v }=(2 \hat{ i }+3 \hat{ j })+(0.3 \hat{ i }+0.2 \hat{ j }) \times 10$
$\Rightarrow \vec{ v }=5 \hat{ i }+5 \hat{ j }$
$v =5 \sqrt{2}$ units
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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