To determine the distance traveled by the stone during the first second of its motion, we need to calculate the stone's initial velocity, final velocity, and the time it takes for the stone to reach its highest point.
Given: Initial velocity (u) = 30 m/s (upwards) Acceleration due to gravity (a) = -10 m/s² (downwards, as it opposes the upward motion)
At the highest point, the final velocity (v) becomes 0 m/s since the stone momentarily stops before falling back down. We can use the equation of motion to calculate the time it takes to reach the highest point:
v = u + at
0 = 30 - 10t
10t = 30
t = 3 seconds
So, it takes 3 seconds for the stone to reach its highest point. Now, to find the distance traveled during the first second, we need to calculate the distance covered during the upward motion (from t = 0 to t = 1) and subtract it from the total distance covered during the upward and downward motion (t = 0 to t = 3).
Using the equation of motion, s = ut + (1/2)at², we can find the distances:
Distance covered during the upward motion from t = 0 to t = 1: s₁ = ut + (1/2)at² s₁ = 30(1) + (1/2)(-10)(1)² s₁ = 30 - 5 s₁ = 25 meters
Distance covered during the upward and downward motion from t = 0 to t = 3: s₂ = ut + (1/2)at² s₂ = 30(3) + (1/2)(-10)(3)² s₂ = 90 - 45 s₂ = 45 meters
Now, we can calculate the distance traveled during the first second: Distance traveled during the first second = s₂ - s₁ Distance traveled during the first second = 45 - 25 Distance traveled during the first second = 20 meters
Therefore, the stone travels a distance of 20 meters during the first second of its motion.