What is the Total Distance Traveled with Zero Acceleration?

In summary, the motion of a particle is defined by x=2(t^3) - 18(t^2) + 48t - 16 where x=meter and t=sec. When the acceleration is zero, the total distance traveled is 44m. To determine this, the particle's velocity must be zero, which occurs at t=4s and t=2s. To find the distance traveled from t=0 to t=3 seconds, the distance traveled from t=0 to t=2 and t=2 to t=3 must be added together.
  • #1
teng125
416
0
the motion of a particle is defined by x=2(t^3) - 18(t^2) + 48t - 16 where x=meter and t=sec.determine the total distance traveled when the acceleration is zero.

the answer is 44m.

pls help...thanx...
 
Physics news on Phys.org
  • #2
Hint:
At what instant (t-value) is the acceleration 0?
 
  • #3
the value t=3 when the acc is zero
 
  • #4
And how may you use that info to answer the original question?
 
  • #5
oh,i found out d.it is the sum of t=0 to 3 rite??
 
  • #6
What do you mean by "sum"?
 
  • #7
the summation
 
  • #8
Another hint: At what time does the particle change direction?
 
  • #9
sorry,i not sure...
 
  • #10
At the moment the particle changes direction, what is its speed?
 
  • #11
the velocity is zero
 
  • #12
Thus, within the interval t=0 to t=3, is there any instant at which the velocity is zero?
 
  • #13
Right. So find when the particle's velocity is zero.
 
  • #14
the particle's velocity = zero when t=4s and 2s
 
  • #15
Right. So to find the distance traveled by the particle from t = 0 to t = 3 seconds find the distance traveled from t = 0 to t = 2 and from t = 2 to t = 3 and add them.
 
  • #16
ya,i found it...thanx...
 

Related to What is the Total Distance Traveled with Zero Acceleration?

1. What is kinematics of particles?

Kinematics of particles is the study of the motion of individual particles without considering the causes of the motion. It involves analyzing the position, velocity, and acceleration of particles as they move through space.

2. What are the basic principles of kinematics of particles?

The basic principles of kinematics of particles include displacement, velocity, and acceleration. Displacement is the change in position of a particle, velocity is the rate of change of displacement, and acceleration is the rate of change of velocity.

3. How is kinematics of particles different from kinematics of rigid bodies?

Kinematics of particles focuses on the motion of individual particles, while kinematics of rigid bodies studies the motion of a group of particles that are fixed together and move as a single unit. Additionally, kinematics of particles does not take into account the size or shape of the particles, while kinematics of rigid bodies considers them.

4. What are the equations used in kinematics of particles?

The main equations used in kinematics of particles are the equations of motion, which include the equations for displacement, velocity, and acceleration. These are often referred to as the "SUVAT" equations, as they stand for displacement (S), initial velocity (U), final velocity (V), acceleration (A), and time (T).

5. How is kinematics of particles applied in real-life situations?

Kinematics of particles is used in a variety of real-life situations, such as analyzing the motion of projectiles in physics, predicting the trajectory of a moving object in sports, and understanding the movement of particles in fluids for engineering and environmental applications. It is also important in fields such as robotics and animation, where the motion of individual particles is crucial in creating realistic movements.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
6K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
392
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
850
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
816
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top