Question

The leader of a bicycle race is traveling with a constant velocity of +11.3 m/s and is 10.2 m ahead of the second-place cyclist. The second-place cyclist has a velocity of +9.00 m/s and an acceleration of +1.20 m/s2. How much time elapses before he catches the leader? Number Units

Answer 1

d = distance between the two cyclist = 10.2 m

v₁ = constant velocity of the leader cyclist = 11.3 m/s

v₂ = velocity of second place cyclist = 9 m/s

a₂ = acceleration of second place cyclist = 1.20 m/s²

let the second -place cyclist catches the leader after time "t"

d₁ = distance travelled by leader cyclist in time "t" = v₁ t

d₂ = distance travelled by second -place cyclist in time "t" = v₂ t + (0.5) a₂ t²

for the second-place cyclist to catch the leader

d₂ = d₁ + d

v₂ t + (0.5) a₂ t² = v₁ t + d

inserting the values

9 t + (0.5) (1.20) t² = (11.3) t + (10.2)

t = 6.5 sec