Final answer:
To determine the distance traveled by a particle with initial velocity of 4 m/s accelerating to 14 m/s in 3 seconds, calculate its acceleration and then apply the displacement formula for constant acceleration, resulting in a distance of 27 meters.
Step-by-step explanation:
To calculate the distance traveled by a particle moving along the x-axis with an initial velocity and a constant acceleration, we can use the kinematic equations for linear motion. The question states that a particle has an initial velocity of 4 m/s and accelerates to 14 m/s in 3 seconds. We need to find the distance it covers in that time.
First, let's find the acceleration using the formula for acceleration (a) when initial (u) and final velocities (v) and the time (t) are known:
a = (v - u) / t
Plugging in the given values:
a = (14 m/s - 4 m/s) / 3 s = 10 m/s² / 3 s = 3.33 m/s²
Now, we can use the formula for displacement (s) with constant acceleration:
s = ut + (1/2)at²
Applying the known values:
s = (4 m/s)(3 s) + (1/2)(3.33 m/s²)(3 s)² = 12 m + 15 m = 27 m
The distance traveled by the particle is 27 meters during the 3-second interval.