Rectilinear Motion with Variable Acceleration Problem No.2 - Kinematics of Particles

TL;DR

Solving a problem on variable acceleration to find displacement, velocity, and acceleration at a given time.

Transcript

hi friends solve problem on variable acceleration let's see what is given in problem the motion of particle along a straight line is governed by the relation a equal to t cube minus 2 t square plus 7 where acceleration a is the acceleration in meters per second square and t is the time in second at time t equal to 1 second the velocity of particle ... Read More

Key Insights

• ❓ The problem involves solving for displacement, velocity, and acceleration using the equation of variable acceleration.
• 🧘 Integration is used to derive the equations of velocity and position from the equation of acceleration.
• 😃 The given conditions, such as velocity at t = 1 second and displacement at t = 0, are used to calculate the constants of integration.

Questions & Answers

Q: What is the equation of acceleration in the problem?

The equation of acceleration is a = t^3 - 2t^2 + 7.

Q: How do you find the equation of velocity?

By integrating the equation of acceleration and substituting the given conditions, the equation of velocity is obtained as v = t^4/4 - (2/3)t^3 + 7t - 3.

Q: How is the equation of displacement derived?

By integrating the equation of velocity and substituting the constant of integration calculated using the given displacement at t = 0, the equation of displacement is derived as x = t^5/20 - t^4/6 + (7/2)t^2 - 3t + 9.

Q: What are the values of acceleration, velocity, and displacement at t = 2 seconds?

At t = 2 seconds, the acceleration is 7 m/s^2, the velocity is 9.67 m/s, and the displacement is 6.93 meters.

Summary & Key Takeaways

• The problem involves solving for displacement, velocity, and acceleration using the equation of variable acceleration.

• The equation of acceleration is given as a = t^3 - 2t^2 + 7.

• By integrating the equation of acceleration, the equations of velocity and position are derived.