Question

A particle is moving in a circle of radius 1.5 m.
Its speed is increasing by 180 rev/minute in one
minute. What is its linear acceleration ?
A) 0.25 m/ s
2 B) 0.30 m/ s
2
C) 0.39 m/ s
2 D) 0.47 m/ s
2

Answer 1

Answer:

see the attached photo for answer

Answer 2

Answer:

The linear accelertaion is $0.47 \mathrm{~m} / \mathrm{s}^{2}$ , so option D is correct.

Explanation:

If the velocity of an object moving in a straight line increases or decreases over time, it is said to be accelerating. Depending on whether the velocity is growing or decreasing, acceleration can be positive or negative.

The velocity of a vehicle can aid in the explanation of linear acceleration. The velocity is measured by the vehicle's speedometer.

Given : $r=1.5 \mathrm{~m}$

$V=\frac{d i s t a n c e}{\text { time }}$

revolution in one min $\frac{\pi }{180}$

Time $1min=60sec$

Distance $=180 \times 2 \pi r$

$v=\frac{d}{v}=\frac{180 \times 2 \pi r}{60}$

$d v=\frac{180 \times 2 \pi r}{60}$

$=6\pi r$            (r=1.5)

$=9\pi$

Now linear accelration $a=\frac{d v}{d t}$

$=\frac{9\pi }{60}$               ( $\pi =3.14$)

$0.47 \mathrm{~m} / \mathrm{s}^{2}$

The linear accelertaion is $0.47 \mathrm{~m} / \mathrm{s}^{2}$