Question

a cyclist moves in a circular path of radius 10m. It takes him 100 seconds to cover 10 laps of the entire path. What is the velocity of the cyclist (in m/s) at the end of 5 seconds?

Answer 1

path length of one lap is given by

$L = 2\pi R$

$L = 2\pi*10[tex]</p><p>[tex]L = 20\pi$

now 10 laps are covered in 100 seconds

total distance moved is given by

$D = 10 L = 200\pi$

now we have

$d = \frac{v_f + v_i}{2}*t$

$200\pi = \frac{vf + 0}{2}*100$

$v_f = 4\pi$

now acceleration is given by

$a = \frac{v_f - v_i}{t}$

$a = \frac{4\pi}{100}$

$a = 0.04\pi$

now velocity after 5 seconds will be

$v_f = v_i + at$

$v_f = 0 + 0.04\pi* 5$

$v_f = 0.20\pi = 0.63 m/s$

so speed at the end of 5 s will be 0.63 m/s