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A body starting from rest moves along a ...

A body starting from rest moves along a straight line with a constant acceleration. The variation of speed (v) with distance (s) is represented by the graph:

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To solve the problem, we need to analyze the motion of a body starting from rest and moving with constant acceleration. We will use the third equation of motion to relate speed (v) and distance (s). ### Step-by-Step Solution: 1. **Identify Initial Conditions**: The body starts from rest, which means the initial velocity \( u = 0 \). 2. **Use the Third Equation of Motion**: The third equation of motion states: \[ v^2 = u^2 + 2as \] Here, \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the constant acceleration, and \( s \) is the distance traveled. 3. **Substitute Initial Velocity**: Since the body starts from rest, we substitute \( u = 0 \) into the equation: \[ v^2 = 0 + 2as \] This simplifies to: \[ v^2 = 2as \] 4. **Rearranging the Equation**: We can rearrange this equation to express \( v \) in terms of \( s \): \[ v = \sqrt{2as} \] 5. **Graphical Representation**: The equation \( v = \sqrt{2as} \) indicates that the relationship between \( v \) and \( s \) is a square root function. If we plot \( v \) against \( s \), the graph will be a curve that opens upwards, resembling a parabola. 6. **Conclusion**: Thus, the variation of speed \( v \) with distance \( s \) is represented by a graph that is symmetric to a parabola. The correct option corresponding to this relationship in the provided choices is option 3.
To solve the problem, we need to analyze the motion of a body starting from rest and moving with constant acceleration. We will use the third equation of motion to relate speed (v) and distance (s). ### Step-by-Step Solution: 1. **Identify Initial Conditions**: The body starts from rest, which means the initial velocity \( u = 0 \). 2. **Use the Third Equation of Motion**: ...
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