Final answer:
To find out how long it takes a runner to stop when decelerating at 2 m/s² from an initial speed of 6 m/s, use the acceleration formula. The final velocity is 0 m/s, and the initial velocity is 6 m/s, leading to a time of 3 seconds to stop.
Step-by-step explanation:
To calculate the time it takes for a runner to stop from an initial speed when decelerating, you can use the formula for acceleration, which in this case is negative because it is actually deceleration:
a = Δv / Δt
Where a is acceleration (or deceleration), Δv is the change in velocity, and Δt is the change in time. We are given an initial velocity of 6 m/s, and deceleration of 2 m/s². Since we want to know the time it takes to come to a stop, the final velocity will be 0 m/s, which means the change in velocity (Δv) is -6 m/s (0 m/s - 6 m/s).
If we rearrange the formula to solve for Δt, we get:
Δt = Δv / a
Plugging in our values gives us:
Δt = -6 m/s / -2 m/s² = 3 s
Therefore, it takes 3 seconds for the runner to come to a complete stop.