I have three word problems i don\'t know how i solve it can you help me please.
ID: 1819508 • Letter: I
Question
I have three word problems i don't know how i solve it can you help me please.
1) The acceleration of a particle traveling along a straight line is a=k/v, where k is a constant. If s=0, v=vo when t=0, determine the velocity of the partical as a function of time t.
2) A partical travels along a straight line with velocity v=(12-3t2)m/s, where t is in seconds. When t=1 s, the particle is located 10m to left of the origin. Detemine the acceleration when t=4 s, the displacement from t=0 to t=10 s, and the distance tha partical travels during this time period.
3) The position of a particle along a straight line is given by s=(1.5t3 _ 13.5t2 + 22.5t) m, where t is in seconds. Determine the position of the particle when t=6 and the total distance it travels during the 6-s time interval. Hint: plot the path to determine the total ditance traveled.
Explanation / Answer
a= k/v dv/dt = k/v Separable DE v dv = k dt Integral (v dv) = Integral (k dt) v^2/2= kt+C v = +/- sqrt( 2kt+C') v(0)=0 0=+/-sqrt(C') C'=0 v=+/-sqrt(2kt) The acceleration is always positive and it starts from rest, so the velocity cannot be negative. v=sqrt(2kt)