17. The displacement of a particle is represented by the following equation : s = 3t3 + 7t2 + 5t + 8 where s is in metre and t in second. The acceleration of the particle at t = 1 s is

17. The displacement of a particle is represented by the following equation : \(s = 3t^3 + 7t^2 + 5t + 8 \) where s is in metre and t in second. The acceleration of the particle at t = 1 s is

(a) \( 14 \; m/s^2 \)

(b) \( 18 \; m/s^2 \)

(c) \( 32 \; m/s^2 \)

(d) \( 0 \; m/s^2 \)

Answer :  (c) \( 32 \; m/s^2 \)

\( s = 3 t^3 + 7 t^2 + 5 t + 8 \)

\( v = \)\( \frac{ds}{dt} \)\( = 9 t^2 + 14 t + 5 \)

\( a = \)\( \frac{dv}{dt} \)\( = 18 t + 14 \)

\( a(1) = 18(1) + 14 = 32\ \text{m/s}^2 \)