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 \(20\pi \,sin \left(\frac\pi{200}\right) m/s\).