Discussion
The linear momentum of a particle as a function of time is given as \(p = (3t^{2} + 2t + 1)\) \(kgms^{-1}\). Then, the force acting on the particle at \(t = 3s\) will be
Answer: A
The force is 20 N.
Newton's second law states that force is the rate of change of momentum:
\[ \begin{aligned} F &= \frac{dp}{dt} = 6t + 2 \\ F(3) &= 18 + 2 = 20\ \text{N} \end{aligned} \]
The constant 1 in \(p\) disappears on differentiating. Putting \(t = 3\) into \(p\) itself gives 34 kg m s-1, a momentum, not a force; 8 N is the value at \(t = 1\).
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