Final answer:
The force acting on a particle with a mass of 1kg and a displacement described by s=2t+3t² is 6 Newtons.
Step-by-step explanation:
The displacement of a particle of mass 1kg is described by s = 2t + 3t². To find the force acting on the particle, we start by finding the acceleration. We do this by differentiating the displacement s twice with respect to time t to get the acceleration a.
First derivative of s with respect to t: ds/dt = v = 2 + 6t
Second derivative of s with respect to t: d²s/dt² = a = 6
Since the acceleration a is constant at 6 m/s², we use Newton's second law of motion, F = ma, to calculate the force:
F = (1 kg)(6 m/s²) = 6 N
Therefore, the force acting on the particle is 6 Newtons.