Question

In a woman’s 100m race, accelerating uniformly, Laura takes 2.0s and Helen 3.0s to obtain their maximum speeds, which they maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4s.

a) What is the acceleration of each sprinter?

b) What are their respective maximum speeds?

c) Which sprinter is ahead at the 6.0s mark, and by how much (distance)?

Answer 1

for Laura :

acc = a1

maximum speed = a t = 2 a1

distance travelled = 0 + a t^2 /2 = a (2^2)/2 = 2 a1

distance remaining = 100 - 2 a1

time remainig = 10.4 -2 = 8.4 s

(100 - 2 a1 ) = (2 a1)(8.4)

100 - 2 a1 = 16.8 a1

a1 = 5.32 m/s^2

For Helen:

v_max = 3 a2

d = a2 (3^2 / 2) = 4.5 a2

100 - 4.5 a2 = (3 a2)(10.4 - 3)

a2 = 3.75 m/s^2

(A) a_Laura = 5.32 m/s^2

a_Helen = 3.75 m/s^2

(B) v_Laura = 5.32 x 2 = 10.6 m/s

v_Helen = 3.75 x 3 = 11.25 m/s

(C) at t = 6

d_Laura = (5.32 x 2^2 / 2) + (10.6 x 4) = 53.04 m

d_Helen = (3.75 x 3^2 / 2) + (11.25 x 3) = 50.6 m

so Laura is ahead by 2.4 m .