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Physics · MOTION IN A STRAIGHT LINE
हिन्दीIn the position-time graph shown in the figure, as the time interval \( \Delta t \) centered at \( t = 4\text{ s} \) is reduced from \( 2\text{ s} \) to an infinitesimally small value, the slope of the chord approaches the slope of the tangent at point \( P \). If the position equation is \( x = 0.08 t^3 \), what is the instantaneous velocity at \( t = 4\text{ s} \)?
Correct answer · Option 4
Instantaneous velocity equal to \( 3.84\text{ m s}^{-1} \)
Explanation
The instantaneous velocity is the derivative of position with respect to time: \( v = \frac{dx}{dt} = \frac{d}{dt}(0.08 t^3) = 0.24 t^2 \). At \( t = 4\text{ s} \), \( v = 0.24 \times 16 = 3.84\text{ m s}^{-1} \).
