The speed of a rain is reduced unformly from 10m/s to 5m/s while covering a distance of 50m.What is its acceleration??
m(1/2)[V2^2 - V1^2] = m a X
(from energy and work considerations)
Cancel the m's
[V2^2 - V1^2] = 2 a X = -75 m^2/s^2
Solve for a, which will be negative in this case.
X = 50 m
V1 and V2 are the initial and final speeds (measured positive down)
a = -0.75 m/s^2
To find the acceleration, we can use the equation for average acceleration:
Acceleration = (Change in Velocity) / (Change in Time)
Here, we know the change in velocity (Δv) is from 10 m/s to 5 m/s, which means the change in velocity is 10 m/s - 5 m/s = 5 m/s.
Next, we need to find the change in time (Δt). We know that the distance traveled (d) is 50 m. We can use the equation:
Distance = (Initial Velocity) * (Time) + (0.5) * (Acceleration) * (Time^2)
Since the initial velocity (u) is 10 m/s, we can rearrange the equation to solve for time:
50 m = (10 m/s) * (Time) + (0.5) * (Acceleration) * (Time^2)
Simplifying the equation:
0.5 * (Acceleration) * (Time^2) + (10 m/s) * (Time) - 50 m = 0
This is a quadratic equation. We can solve it using the quadratic formula:
Time = [-b ± √(b^2 - 4ac)] / (2a)
Here, a = 0.5, b = 10 m/s, and c = -50 m. Plugging in these values, we get:
Time = [-10 m/s ± √((10 m/s)^2 - 4 * 0.5 * (-50 m))] / (2 * 0.5)
Simplifying further:
Time = [-10 m/s ± √(100 m²/s² + 100 m²/s²)] / (1 m/s)
Time = [-10 m/s ± √(200 m²/s²)] / (1 m/s)
Time = [-10 m/s ± 14.14 m/s] / (1 m/s)
Now, we have two possible values for time:
1. Time = (-10 m/s + 14.14 m/s) / (1 m/s) = 4.14 s
2. Time = (-10 m/s - 14.14 m/s) / (1 m/s) = -24.14 s
Since time cannot be negative, we take the positive value: Time = 4.14 s.
Now, we can substitute this value back into the equation for acceleration:
Acceleration = (Change in Velocity) / (Change in Time)
Acceleration = (5 m/s) / (4.14 s)
Acceleration ≈ 1.21 m/s^2
Therefore, the acceleration of the rain is approximately 1.21 m/s².
To find the acceleration of the rain, we need to use the formula for acceleration:
Acceleration (a) = change in velocity (Δv) / time taken (Δt)
In this case, the rain starts with an initial velocity (u) of 10 m/s and ends with a final velocity (v) of 5 m/s. Therefore, the change in velocity (Δv) is:
Δv = v - u
= 5 m/s - 10 m/s
= -5 m/s
The negative sign indicates that the velocity decreased or reduced.
The rain covers a distance of 50 meters. However, the distance doesn't affect the calculation of acceleration, it only tells us how far the rain travels.
Since we don't have any information about the time it takes for the rain speed to change, we cannot calculate the acceleration accurately. Acceleration depends on time, and without the time component, we can't find the acceleration of the rain in this situation.
Therefore, we can't determine the acceleration of the rain with the given information.