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In first second of an object dropped fro...

In first second of an object dropped from some height, the distance by which it will fall is `("take g = 10 "ms"^(–2))`

A

5m

B

10m

C

2.5m

D

15m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of finding the distance an object falls in the first second after being dropped from a height, we can use the equations of motion under uniform acceleration. Here are the steps to arrive at the solution: ### Step-by-Step Solution: 1. **Identify the Given Values:** - Initial velocity (u) = 0 m/s (since the object is dropped) - Acceleration (a) = g = 10 m/s² (acceleration due to gravity) - Time (t) = 1 second (the time interval we are considering) 2. **Use the Equation of Motion:** The equation for displacement (s) under uniform acceleration is given by: \[ s = ut + \frac{1}{2} a t^2 \] 3. **Substitute the Known Values:** Since the initial velocity (u) is 0, the equation simplifies to: \[ s = 0 \cdot t + \frac{1}{2} g t^2 \] Substituting the values of g and t: \[ s = \frac{1}{2} \cdot 10 \cdot (1)^2 \] 4. **Calculate the Displacement:** \[ s = \frac{1}{2} \cdot 10 \cdot 1 = \frac{10}{2} = 5 \text{ meters} \] 5. **Conclusion:** The distance fallen by the object in the first second is **5 meters**.
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