Question

Please check if right

2t+1|₀²=[2(2)+1]−[2(0)+1]=4
Use integration to determine the formula for the "equation of motion" r(t), given that:
r'(t)=

Answer 1

To find the equation of motion in Physics, integrate the velocity function component-wise with respect to time. Each term of the velocity function, when integrated, will yield the corresponding term of the position function, r(t).

Step-by-step explanation:

The question regards Physics, specifically kinematics in the context of motion under constant acceleration. To find the equation of motion (r(t)) for a particle when given its velocity function (r'(t)), one must integrate the velocity function with respect to time. This integration process yields the displacement, or position function, which describes how the particle's position changes over time.

From the provided velocity function dr(t)/dt = 4.0tî + 3.0ķ + 5.0k m/s, we can integrate each component with respect to time to find the corresponding components of r(t). For example, integrating 4.0t with respect to time yields 2.0t2. Integrating constants with respect to time yields a linear term; that is, the integration of 3.0 with respect to t gives 3.0t. Since no initial position is given, we cannot include a constant term, unless one is specified elsewhere.