Rectilinear Motion with Variable Acceleration - Problem 6 - Kinematics of Particles

TL;DR

This content discusses a problem on variable acceleration, including finding deceleration and position at a specific time, calculating the distance traveled during a time interval, and determining the average speed.

Transcript

hi friends we'll solve problem on variable acceleration see what is given in problem the velocity of a particle traveling in a straight line is rectilinear motion is given by v equal to 60 minus 3t square that means velocity is given as a function of time t where t is in seconds some boundary condition is given if s equal to 0 when t equal to 0 wha... Read More

Key Insights

• 🧘 The problem involves solving for deceleration and position using given equations of velocity and time.
• 🧘 Differentiation of the velocity equation gives acceleration as a function of time, while integration gives the equation of position.
• 🗺️ The distance traveled is found by dividing the time interval and calculating the displacements in each part.
• 🐎 Average speed is obtained by dividing the distance traveled by the time interval.
• 🤘 The negative sign in the calculated deceleration indicates deceleration.
• 🧘 The position at t=2 seconds is found using the equation of position to determine the distance traveled in the first time interval.
• 🧘 The position at t=0 and t=3 seconds is zero, indicating a change in direction of motion.

Questions & Answers

Q: How do we find the deceleration of the particle?

To find the deceleration, we differentiate the equation of velocity with respect to time, resulting in acceleration as a function of time. Substituting t=3 seconds in the equation yields a deceleration of -12 meters per second squared.

Q: How do we determine the position of the particle at t=3 seconds?

By integrating the equation of velocity with respect to time, we obtain the equation of position. Substituting t=3 seconds in this equation gives a position of zero meters.

Q: How do we calculate the distance traveled during the three-second time interval?

We divide the time interval (0 to 3 seconds) into two parts: 0 to 2 seconds and 2 to 3 seconds. We calculate the displacements in each part by subtracting the initial position from the final position. The sum of these displacements gives the distance traveled, which is 8 meters.

Q: What is the average speed of the particle?

Average speed is calculated by dividing the distance traveled by the time interval. In this case, the average speed is 2.67 meters per second.

Summary & Key Takeaways

• The problem involves finding the deceleration and position of a particle at time t=3 seconds, given its velocity as a function of time.

• The distance traveled during a three-second time interval is calculated by dividing it into two time intervals and finding the displacements in each interval.

• The average speed is determined by dividing the distance traveled by the time interval.