Question

A skater picks up speed as she starts skating. Her speed increases from 2m/sec to 10m/s while traveling a distance of 45m. What is the rate at which the skaters speed changed? Round your answer to nearest whole number.

Answer 1

The rate at which the skater's speed changed, or acceleration, is 1 m/s^2 when rounded to the nearest whole number.

Step-by-step explanation:

The rate at which the skater's speed changed can be determined by calculating the acceleration over the distance covered. Acceleration (a) is defined as the change in velocity (Δv) divided by the time taken (Δt) for that change. To find the acceleration, we first need to assume constant acceleration and use the kinematic equation:

v^2 = u^2 + 2as

Where v is the final velocity, u is the initial velocity, s is the distance, and a is the acceleration. Plugging in the values:

10^2 = 2^2 + 2 · a · 45

100 = 4 + 90a

96 = 90a

a = 96 / 90

a = 1.067 m/s^2

Rounded to the nearest whole number, the rate at which the skater's speed changed is 1 m/s^2.