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Physics · MOTION IN A STRAIGHT LINE
हिन्दीThe position of an object moving along the x-axis is given by \( x = a + b t^2 \), where \( a = 8.5\text{ m} \) and \( b = 2.5\text{ m s}^{-2} \). What is the ratio of its average velocity between \( t = 2.0\text{ s} \) and \( t = 4.0\text{ s} \) to its instantaneous velocity at \( t = 2.0\text{ s} \)?
Correct answer · Option 1
\( 1.5 \)
Explanation
Average velocity \( \bar{v} = \frac{x(4) - x(2)}{4 - 2} = \frac{(8.5 + 2.5 \times 16) - (8.5 + 2.5 \times 4)}{2} = \frac{30}{2} = 15\text{ m s}^{-1} \). Instantaneous velocity \( v(t) = \frac{dx}{dt} = 2bt = 5t \). At \( t = 2.0\text{ s} \), \( v(2) = 10\text{ m s}^{-1} \). Ratio = \( \frac{15}{10} = 1.5 \).
