# Net Change: Motion on a Line

Net change, within the realm of motion on a line, encapsulates the fundamental concept of measuring the overall shift in position over a specified interval. It serves as a pivotal metric in understanding the dynamics of objects in motion, particularly along a linear trajectory. This concept focuses solely on the final position relative to the initial position, disregarding any intermediate fluctuations. Analyzing net change provides crucial insights into the displacement of objects and is foundational in various fields such as physics, calculus, and engineering, where precise tracking of motion is paramount.

Questions

- A particle is constrained to move in #Q_1#, in a parabolic groove # y = x^2#. It was at O, at t = 0 s. At time t s, its speeds in the directions Ox and Oy are 5 and 12 cm/s, respectively. How do you prove its direction makes #67^o22'49''# with Ox?
- How do you find the speed of a particle that moves along a line?
- What is the farthest apart the particles ever get if the positions of two particles on the s-axis are #s_1=cos(t)# and #s_2=cos(t+pi/4)#?
- Calculate the work done by a particle under the influence of a force #y^2 hat(i) - x^2hat(j)# along the curve #y=4x^2# from #(0,0)# to #(1,4)#?
- How do you find the stationary points of a particle that moves along a line?
- How do you find the velocity of a particle that moves along a line?
- How many values of t does the particle change direction if a particle moves with acceleration #a(t)=3t^2-2t# and it's initial velocity is 0?
- How do you find the position function #x(t)# if you suppose that the mass in a mass-spring-dashpot system with #m=25#, #c=10# and #k=226# is set in motion with #x(0)=20# and #x'(0)=41#?
- What is the position of a particle at time #t=2# if a particle moves along the x axis so that at any time #t>0#, the velocity is given by #v(t)=4-6t^2#, and at position #x=7# at #t=1#?
- How do you solve the AP Calculus AB 2013 Free Response question #2? http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_calculus_ab.pdf
- How do you find the instantaneous velocity for the particle whose position at time #t# is given by #s(t)=3t^2+5t# ?
- How do you find the displacement of a particle that moves along a line?
- The acceleration of a particle at time #t# seconds is given by # a = 6t#. Given that #v=10# when #t=0# and that #x=7# when #t=0# find #x# when #t=2#?
- How do you find the total displacement for the particle whose position at time #t# is given by #s(t)=3t^2-5t# on the interval #0<=t<=2#?
- An object moves so that at time t its position s is found using #s(t) = 5*cos(t)#. For what values of 't' does the object change direction?
- Consider a particle moving along the x-axis where x(t) is the position of the particle at time t A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t)=5cos(t). At t=0, its position is x=2?
- How do you find the total distance traveled by a particle that moves along a line?
- How do you find the instantaneous acceleration for the particle whose position at time #t# is given by #s(t)=3t^2+5t# ?
- Rates of Change Question. How to do this?
- How do you solve 2015 AP Calculus AB Question #1?