Question:
A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10\, s$ is
A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10\, s$ is
Updated On: Jul 5, 2022
- $10$ units
- $7\sqrt{2}$ units
- $7$ units
- $8.5$ units
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The Correct Option is B
Solution and Explanation
$\overrightarrow{u}=3\hat{i}+4\hat{j} ; \overrightarrow{a}=0.4\hat{i}+0.3\hat{j}$
$\overrightarrow{u}=\overrightarrow{u}+\overrightarrow{a}t$
$=3\hat{i}+4\hat{j}+\left(0.4\hat{i}+0.3\hat{j}\right)10=3\hat{i}+\hat{j}+4\hat{i}+3\hat{j}=7\hat{i}+7\hat{j}$
Speed is $\sqrt{7^{2}+7^{2}}=7\sqrt{2}$ 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