To determine the rock's acceleration, we can use the formula for average acceleration:
acceleration (a) = (final velocity - initial velocity) / time
In this case, the initial velocity (u) is 10 m/s, the final velocity (v) is 40 m/s, and the time (t) is 2 seconds. Plugging these values into the formula, we get:
a = (40 m/s - 10 m/s) / 2 s = 30 m/s / 2 s = 15 m/s²
So the rock's acceleration is 15 m/s².
To calculate the distance the rock traveled in 5 seconds, we can use the formula for distance covered in uniformly accelerated motion:
distance (d) = initial velocity (u) * time (t) + (1/2) * acceleration (a) * time squared (t²)
In this case, the initial velocity (u) is 10 m/s, the time (t) is 5 seconds, and the acceleration (a) is 15 m/s². Plugging these values into the formula, we get:
d = 10 m/s * 5 s + (1/2) * 15 m/s² * (5 s)² = 50 m + (1/2) * 15 m/s² * 25 s² = 50 m + 187.5 m = 237.5 m
So the rock traveled a distance of 237.5 meters in 5 seconds.
To find the rock's velocity after 10 seconds of falling, we can again use the formula for uniformly accelerated motion:
v = u + a * t
In this case, the initial velocity (u) is 10 m/s, the acceleration (a) is 15 m/s², and the time (t) is 10 seconds. Plugging these values into the formula, we get:
v = 10 m/s + 15 m/s² * 10 s = 10 m/s + 150 m/s = 160 m/s
So the rock's velocity after 10 seconds of falling is 160 m/s.