Particle Motion: Zero Velocity and Distance Traveled at x=0

In summary, motion is the change in position of an object over time. There are three main types of motion: linear, rotational, and oscillatory. Speed measures how fast an object is moving, while velocity takes into account both speed and direction. Acceleration is the rate of change of an object's velocity over time. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be.
  • #1
Alexanddros81
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Homework Statement


11.8 The motion of a particle is defined by the relation ##x=t^3 - 6t^2 - 36t - 40,
where x and t are expressed in feet and seconds, respectively. Determine
(a) when the velocity is zero, (b) the velocity, the acceleration, and the total
distance traveled when x = 0.

Homework Equations

The Attempt at a Solution



Vector Mechanics Dynamics Beer P11_8 s.jpg

[/B]
Can you check my solution?
 

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  • #2
It all looks correct to me. I'm not sure why you found the time when ##a = 0## or the position at that time.
 
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Related to Particle Motion: Zero Velocity and Distance Traveled at x=0

1. What is the definition of motion?

Motion is the change in position of an object over time.

2. What are the different types of motion?

The three main types of motion are linear motion (movement in a straight line), rotational motion (movement around an axis), and oscillatory motion (back and forth movement).

3. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In other words, velocity takes into account the object's speed and the direction it is moving in.

4. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It can be calculated by dividing the change in velocity by the change in time.

5. How does force affect the motion of a particle?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be.

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