1. particle has a=2-2x, initially v=4m/s , x=0
a)find v in terms of x
what i got was v=(16+4x-2x^2)^1/2 how do i know whether v is positive or negative
b) find the greatest v
do i normally just let a=0 for min/max velocity
what do i have to do if the ques asks for max/min acceleration
particle starts from the origin and has
v=cos^2(x)
a= -2sin(x)*cos^3(x)
x= tan^-1(t) inverse
where 0<=x<π
Describe the motion of particle from its initial position to its limiting position (2 marks)
the graph i get for displacement vs time is an inverse tangent curve with range: 0<=y<π/2
Im not sure what's required for questions that ask me to describe the motion
the answer i wrote was: the particle is moving to the right of origin with a speed that is increasing at a decreasing rate
Hey! Can't say I fully understand what you're actually asking, but I'll have a go.
I assume you're asking how to tell whether, when you square root v, you should make the equation positive or negative. Essentially, you just sub a point in and see which one works; in this case, you were right to choose the positive route as initially the particle is moving to the right (velocity is positive, so it is assumed to be moving right).
In terms of finding the maximum and minimum velocity/acceleration etc. for questions like this, you usually let the particle be at its endpoints or center. Unlike classical motion (ie, 2U stuff), it becomes increasingly difficult to just differentiate for t and find a standard max/min. Instead, we just have to remember that maximum velocity will occur when the particle is at the center of motion, and maximum acceleration will occur when the particle is at its endpoints (ie. either side of its motion).
Your second question is absolutely right; all that's being asked is a general description of displacement, velocity and acceleration! Plus, you did it in a succinct and mathematically accurate way
Jake