Final answer:
The acceleration of the particle is -1.3 m/s², its initial velocity is 18.0 m/s, and the instant when its velocity is zero is approximately 13.8 s.
Step-by-step explanation:
To find the acceleration of the particle, we can use the formula: acceleration (a) = change in velocity / change in time. From the given information, the particle's velocity changes from 5.0 m/s to -8.0 m/s, and the time changes from 10 s to 20 s. So, the change in velocity is -8.0 m/s - 5.0 m/s = -13.0 m/s and the change in time is 20 s - 10 s = 10 s. Therefore, the acceleration is a = -13.0 m/s / 10 s = -1.3 m/s².
To find the initial velocity of the particle, we can use the formula: initial velocity (u) = final velocity (v) - acceleration (a) * time (t). We know that at t = 10 s, the velocity is 5.0 m/s. So, using the given values of v = 5.0 m/s, a = -1.3 m/s², and t = 10 s, we can calculate the initial velocity: u = 5.0 m/s - (-1.3 m/s²) * 10 s = 5.0 m/s + 13.0 m/s = 18.0 m/s.
To find the instant when the particle's velocity is zero, we can use the formula: final velocity (v) = initial velocity (u) + acceleration (a) * time (t). Since we want the velocity to be zero, we can set v = 0 and rearrange the formula to solve for t: t = (v - u) / a. Plugging in the values of v = 0 m/s, u = 18.0 m/s, and a = -1.3 m/s², we can calculate the time: t = (0 m/s - 18.0 m/s) / -1.3 m/s² = 18.0 m/s / 1.3 m/s² ≈ 13.8 s.