Final answer:
The person decelerates at -4 m/s² from an initial velocity of 3 m/s for 3 seconds and covers a distance of 9 meters. The negative sign in the calculation indicates the direction of motion.
Step-by-step explanation:
To calculate the distance traveled by a person initially moving at 3 m/s and accelerating at -4 m/s² for 3 seconds, we use the kinematic equation for distance covered under constant acceleration, which is:
s = ut + ½at²
Here, u is the initial velocity, a is the acceleration, and t is the time elapsed. Substituting the given values, we have:
s = (3 m/s)(3 s) + ½(-4 m/s²)(3 s)²
Calculating this yields:
s = 9 m - 18 m
s = -9 m
The person will have traveled a distance of 9 meters after 3 seconds, with the negative sign indicating the direction opposite to the initial direction of motion due to the deceleration. Please note that in a real-world situation, the distance covered cannot be negative; we're interested in the magnitude, which is 9 meters.