Question:
A particle moves in a circle of radius 20 cm. Its linear speed is given by v = 2t . where t is in s and v in m/s. Then
A particle moves in a circle of radius 20 cm. Its linear speed is given by v = 2t . where t is in s and v in m/s. Then
Updated On: Mar 26, 2024
- the radial acceleration at $ t = 2s is 80ms^{-2}$
- tangential acceleration at $t = 2s is 2 ms^{-1}$
- net acceleration at t = 2 s is greater than 80 $ms^{-1}$
- tangential acceleration remains constant in magnitude
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The Correct Option is D
Solution and Explanation
v = 2t, $a_c = \frac{\nu^2}{r} = \frac{(2t)^2}{0.2}$ = 20t$^2$ = 20 $\times 2^2$ = 80 m/s$^2$
$a_t = \frac{dv}{dt} $ = 2 m/s$^2$
Net acceleration : a = $\sqrt{a^2_c + a_t^2} $ > 80 m/s$^2$
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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