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Motion of a particle is given by equation $S = (3t^3 + 7t^2 + 14t + 8)$ m. The value of acceleration of the particle at t = 1 sec is :
A
10 m/s$^2$
B
32 m/s$^2$
C
23 m/s$^2$
D
16 m/s$^2$
Detailed Solution
$v = \dfrac{ds}{dt} = \dfrac{d}{dt}(3t^3 + 7t^2 + 14t + 8) = 9t^2 + 14t + 14$
$a = \dfrac{dv}{dt} = 18t + 14$
At t = 1 s: $a = 18 + 14 = 32$ m s$^{-2}$
$a = \dfrac{dv}{dt} = 18t + 14$
At t = 1 s: $a = 18 + 14 = 32$ m s$^{-2}$