To find the distance traveled by the object, we can use the kinematic equation:
d = v₀t + (1/2)at²,
where: d is the distance traveled, v₀ is the initial velocity, t is the time, a is the acceleration.
Given: Initial velocity, v₀ = 4 m/s, Time, t = 3 s, Final velocity, v = 14 m/s.
We need to find the acceleration first. We can use the following equation:
v = v₀ + at,
Rearranging the equation, we get:
a = (v - v₀) / t.
Substituting the values:
a = (14 m/s - 4 m/s) / 3 s a = 10 m/s / 3 s a ≈ 3.33 m/s².
Now we can calculate the distance traveled:
d = v₀t + (1/2)at².
Substituting the given values:
d = (4 m/s) * (3 s) + (1/2) * (3.33 m/s²) * (3 s)² d = 12 m + (1/2) * 3.33 m/s² * 9 s² d = 12 m + 15 m d = 27 m.
Therefore, the object traveled a distance of 27 meters during this time. Option (A) 27 m is the correct answer.