Question

At t=0, a particle starts from rest and moves in the xy space with an acceleration a=(4 i+6j)m/s . Determine the velocity and position of the particle as a function of time.

Answer 1

To determine the velocity and position of the particle as a function of time, integrate the given acceleration function. The velocity v(t) is the integral of the acceleration function, and the position function r(t) is the integral of the velocity function.

Step-by-step explanation:

Kinematics is the study of the motion of mechanical points, bodies and systems without consideration of their associated physical properties and the forces acting on them. The study is often referred to as the geometry of motion, and it models these motions mathematically using algebra.

To determine the velocity and position of the particle as a function of time, we need to integrate the given acceleration function. The velocity v(t) can be found by integrating the acceleration function a(t) concerning time: v(t) = ∫ a(t) dt. Plugging in the values of the acceleration function a(t) = (4i + 6j)m/s, we can integrate component-wise to find v(t) = (4ti + 6tj) + C, where C is the constant of integration.

To find the position function, we integrate the velocity function v(t) concerning time: r(t) = ∫ v(t) dt. Integrating component-wise, we get r(t) = (2t^2i + 3t^2j) + C1t + C2, where C1 and C2 are the constants of integration.