A rock is thrown straight down with an initial velocity of 14 m/s from a cliff. What is the rock’s
displacement after 2.0 s?
after 2.0 s the rock has been accelerated by gravity ... vf = 14 + (2 * g) m/s
the average velocity is ... (vi + vf) / 2
displacement is ... (average velocity) * time
rock is thrown straight down with an initial velocity of 14 m/s from a cliff. What is the rock’s
displacement after 2.0 s?
To find the rock's displacement, we need to find the distance traveled by the rock in the vertical direction after 2.0 seconds.
In this case, the rock is thrown straight down, so we can assume that the acceleration due to gravity is acting in the negative direction.
The displacement can be calculated using the following equation:
displacement = initial velocity * time + (1/2) * acceleration * (time^2)
Given:
Initial velocity (u) = 14 m/s (since it is thrown downward, the initial velocity has a negative sign)
Time (t) = 2.0 s
Acceleration (a) = -9.8 m/s^2 (gravity)
Plugging these values into the equation, we have:
displacement = (-14 m/s) * (2.0 s) + (1/2) * (-9.8 m/s^2) * (2.0 s)^2
Simplifying the equation:
displacement = (-28 m) + (-9.8 m/s^2) * (2.0 s)^2
displacement = -28 m + (-9.8 m/s^2) * 4.0 s^2
displacement = -28 m + (-9.8 m/s^2) * 16 s^2
displacement = -28 m + (-9.8 m/s^2) * 16 s^2
displacement = -28 m - 156.8 m
displacement = -184.8 m
Therefore, the rock's displacement after 2.0 seconds is -184.8 meters. The negative sign indicates that the rock is moving in the downward direction.
To find the rock's displacement after 2.0 seconds, we can use the formula for displacement:
Displacement = Initial velocity × Time + 0.5 × Acceleration × Time^2
In this case, the initial velocity of the rock is 14 m/s, and we can assume the acceleration due to gravity is -9.8 m/s^2 (negative because it is acting downward). Therefore, we can substitute these values into the equation:
Displacement = (14 m/s) × (2.0 s) + 0.5 × (-9.8 m/s^2) × (2.0 s)^2
Now let's calculate the displacement:
Displacement = (14 m/s) × (2.0 s) + 0.5 × (-9.8 m/s^2) × (4.0 s^2)
Displacement = 28 m + 0.5 × (-9.8 m/s^2) × (4.0 s^2)
Displacement = 28 m + (-19.6 m/s^2) × (4.0 s^2)
Displacement = 28 m + (-78.4 m)
Displacement = -50.4 m
So, the rock's displacement after 2.0 seconds is -50.4 meters. The negative sign indicates that the displacement is in the downward direction.