Question

An athlete jogs at a constant angular velocity of 0.150 rad/s around a circular track. At time t = 0, she passes a stationary runner, who immediately starts chasing her with a constant angular acceleration of 0.225 rad/s2. At what time will the second runner have caught up to the first runner?

Answer 1

given

= 0.15 rad/sec

angular acceleration of 0.225 rad/sec² =

using equations for distance is d₁ = t

same way d₂ = 1/2 t²

d₁ = d₂

t = 1/2 t²

= 1/2 t

t = 2 /

= 2 x 0.15 / 0.225

t = 1.34 sec

the second runner have caught up to the first runner in t = 1.34 sec.