Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Equation of displacement for any particle is $s = 3t^3 + 7t^2 + 14t + 8$ m. Its acceleration at time $t = 1$ sec is:

10 m/s²

16 m/s²

25 m/s²

32 m/s²

Velocity ( $v$ ): Instantaneous velocity is the rate of change of displacement, $v = \frac{ds}{dt}$ . Given $s = 3t^3 + 7t^2 + 14t + 8$ . Differentiating with respect to $t$ : $v = \frac{d}{dt}(3t^3 + 7t^2 + 14t + 8) = 9t^2 + 14t + 14$ .
Acceleration ( $a$ ): Instantaneous acceleration is the rate of change of velocity, $a = \frac{dv}{dt}$ . Differentiating $v$ with respect to $t$ : $a = \frac{d}{dt}(9t^2 + 14t + 14) = 18t + 14$ .
Calculation at $t = 1$ sec: Substitute $t = 1$ into the acceleration equation: $a = 18(1) + 14 = 32 \text{ m/s}^2$ .

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