Question

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. \(16\  m/s\)

Answer 1

The Correct Option is B

\(v =\frac {ds}{dt}\)

\(v = \frac {d}{dt} (3t^3+7t^2+14t+8)\)

\(v =9t^2+14t+14\)

\(a=\frac {dv}{dt}\)

\(a =\) \(\frac {d}{dt}( 9t^2+14t+14)\)

\(a =18t+14\)

\(at,\ t=1\ sec\)

\(a=32\ ms^{-2}\)

So, the correct option is (B): \(32 \ m/s^2\)