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A particle is moving on a circle of radius 1 km with constant speed 10π m/s. Find the change in velocity vector of particle in a time duration of 1 second (in m/s). (change in velocity = vf - vi)​

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Given that,

Radius of circle = 1 km

Speed = 10π m/s

Time = 1 sec

The velocity is negative in opposite direction in same level .

The velocity at half revolution is

vf = -10π m/s

We need to calculate the arc

arc = distance

Using formula of arc

D = v x t

Put the value into the formula

D = 10π x 1

D = 10π m

We need to calculate the angle

Using formula of angle

\(\theta = \frac DR\)

Where, D = arc

R = radius

Put the value into the formula

\(\theta = \frac{10π}{1000}\)

\(\theta = \frac\pi{100} rad\)

We need to calculate the change in velocity

Using formula of change in velocity

Hence, The change in velocity is \(20\pi \,sin \left(\frac\pi{200}\right) m/s\).

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