Dinámica. Video 1. Cálculo diferencial aplicado a la cinemática de una partícula

Problem 11.1 The motion of a particle is defined by the relation: x = 1.5t⁴ − 30t² + 5t + 10, where x and t are expressed in meters and seconds, respectively. Determine the position, velocity, and acceleration of the particle when t = 4 s. In this video, we solve a kinematics problem for a particle step by step using derivatives. Starting with the position function: x(t) = 1.5t⁴ − 30t² + 5t + 10 we determine the position, velocity, and acceleration of the particle when t = 4 s. You will learn to: ✅ Evaluate the position function. ✅ Obtain the velocity by differentiating the position function. ✅ Calculate the acceleration by differentiating the velocity function. ✅ Correctly interpret the results and their units. Results: 📌 Position: x(4) = -66 m 📌 Velocity: v(4) = 149 m/s 📌 Acceleration: a(4) = 228 m/s² Subscribe to INGPASOAPASO to learn dynamics, statics, strength of materials, and structural design through step-by-step solved exercises. #Kinematics #Dynamics #Derivatives #Position #Velocity #Acceleration #CivilEngineering #INGPASOAPASO