You are here:
- Home
- Teens
- Homework/Study Tips
- Calculus
- Particle Motion
Calculus/Particle Motion
Advertisement
Question
A particle moves along a so that its position at any time t(greater than or equal to) 0 is given by the function
s(t)= t^2- 3t + 2,
where s is measured in meters and t is measured in seconds.
(a) Find the displacement during the first 5 seconds.
(b) Find the average velocity during the first 5 seconds.
(c) Find heinstananeours velocity when t=4.
(d) Find he acceleration of the paticle when t=4.
(e) At what values of t does the particle chang direction?
(a) Displacement=s(5)-s(0)=5^2-3*5+2-[0^2-3*0+2]=25-15=5 meters.
(b) Average velocity=Displacement/5 sec = 5/5 =1 m/s .
(c) Instananeours velocity=s'(t) at t=4 :
s'(t)=2t-3 . s'(4)=2*4-3=3m/s .
(d) Acceleration=s''(t)=2 m/s^2 .
(e) The particle changes direction when the velocity changes sign :
Meaning, when s'(t)=0 : 2t-3=0 --> t=1.5 sec .
The particle is moving forward in the interval 0<t<1.5 sec
And is moving backward in the interval 1.5<t
Alon.
Related Articles
- 2009 SEC Football Preview - SEC Football Preview 2009
- 2010 SEC Football Preview - SEC Football Preview 2010 - 2010 SEC Football Predictions
- Slope of a Line - What is the Slope of a Linear Function
- Orlando Bloom Interview - Pirates of the Caribbean Dead Man's Chest, Johnny Depp, His Inner Pirate
- One-Dimensional Kinematics: Motion Along a Straight Line
Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience
1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
©2012 About.com, a part of The New York Times Company. All rights reserved.