Question:
A body is moving with velocity $30\, ms$ towards east After 10 s its velocity becomes $40 \,ms$ towards north. The average acceleration of the body is
A body is moving with velocity $30\, ms$ towards east After 10 s its velocity becomes $40 \,ms$ towards north. The average acceleration of the body is
Updated On: May 21, 2024
- $7\, ms^{-1}$
- $\sqrt{7}\,ms^{-1}$
- $5\,ms^{-1}$
- $1 \,ms^{-2}$
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The Correct Option is C
Solution and Explanation
Average acceleration
$\vec{ A }_{\text {avg }}=\frac{\vec{ v }_{ f }-\vec{ v }_{ i }}{ t }=\frac{40 \,\hat{ j }-30 \,\hat{ i }}{10} $
$\vec{ A }_{\text {avg }}=\frac{\sqrt{40^{2}+30^{2}}}{10}=5 \,m / \,sec ^{2}$
$\vec{ A }_{\text {avg }}=\frac{\vec{ v }_{ f }-\vec{ v }_{ i }}{ t }=\frac{40 \,\hat{ j }-30 \,\hat{ i }}{10} $
$\vec{ A }_{\text {avg }}=\frac{\sqrt{40^{2}+30^{2}}}{10}=5 \,m / \,sec ^{2}$
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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