In a 100. m race, Lisa crosses the finish line after 11.3 s. Accelerating uniformly, Lisa took 1.85 s to attain maximum speed, which she maintained for the rest of the race. What was Lisa's acceleration?

acceleration = 5.21 m/s²

Explanation:

given data

distance d = 100 m

time v = 11.3 s

max speed time u = 1.85 s

to find out

acceleration a

solution

we know initial speed is zero

and after 1.85 s lisa run 11.3 s

so we consider after 1.85 s lisa run at constant speed that is 11.3 - 1.85 = 9.45 s

we consider lisa run with velocity x

so velocity

V = u + at

x = 0 + a (1.85)

a = x / 1.85 m/s² ... 1

and distance travel with x = speed * time

distance at x velocity = 9.45 x ... 2

now calculate the distance to reach at maximum speed by distance formula

distance = ut + 1/2 * at²

distance = 0 + 1/2 * (x/1.85) (1.85) ²

distance = 0.925 x meters ... 3

so from equation 2 and 3

total distance = 0.925 x + 9.45 x

100 = 0.925 x + 9.45 x

so x = 9.6385 m/s

so from equation 1

a = x / 1.85 m/s²

a = 9.6385 / 1.85 m/s²

a = 5.21 m/s²