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