Starting from rest, a runner at a track meet reaches a speed of 7.5 m/s in 1.7 s. how far does she run during this time, assuming her acceleration is uniform?

For this problem, we use the equations derived for rectilinear motion at constant acceleration. The equations are:

a = (v - v₀)/t
x = v₀t + 0.5at²
where
a is acceleration
v and v₀ are the final and initial velocities, respectively
x is the distance
t is the time

First, let's determine the a to be used in the second equation:

a = (7.5 m/s - 0 m/s)/1.7 s = 4.411 m/s²
x = (0)(1.7s) + 0.5(4.411 m/s²)(1.7 s)²
x = 6.375 m