Question:
A car is moving in a circular path of radius 500 m with a speed of 30 $ms^{-1}$. If the speed is increasing at the rate of 2 $ms^{-2}$ the resultant acceleration will be
A car is moving in a circular path of radius 500 m with a speed of 30 $ms^{-1}$. If the speed is increasing at the rate of 2 $ms^{-2}$ the resultant acceleration will be
Updated On: Jul 5, 2022
- 2 $ms^{-2}$
- 2.5 $ms^{-2}$
- 2.7 $ms^{-2}$
- 4 $ms^{-2}$
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The Correct Option is C
Solution and Explanation
Car will have two types of acceleration
Radial acceleration,
$a =\frac{v^2}{r} = \frac{30 \times 360}{500} = 1.8$
Tangential acceleration
$a_r= 2\,ms^{-2}$
= Net acceleration
$a = \sqrt{a_r^2 +a_r^2}$
= $\sqrt{(1.8)^2 + (2)^2 } = \sqrt{7.24}$
= 2.69
= 2.7 $ms^{-2}$
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Notes on Motion in a plane
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