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