10 .A particle moving along a straight line starts at time t=0 seconds with a velocity 4m/s .At any subsequent time t seconds the acceleration of the particle is (6t-8)m/s^(2) .Find
(a) the distance the particle moves before first coming to instantaneous rest.
(b) the total time T seconds taken by the particle to return to the starting point.
(c) the greatest speed of the particle for 0<=t<=T .
Answers
Answer: a particle moves along a straight line and its position at time t is given by s(t)t3−3.5t24t
=1+5 where s is measured in feet and t in seconds, consider t in the interval [0,inf)
what is the particles position at time 4?
what is the velocity at time t? (making a formula)
what is the velocity at time 4?
the particle stops moving at two times, a and b, what are these times?
when is the particle moving in the positive direction? using interval notation
when is the particle moving in the negative direction? using interval notation
total distance traveled between time 0 and 7?
acceleration at time t? (making a formula)
acceleration at time 4?
when is the particle speeding up?(interval notation)
slowing down? (interval notation)
Explanation: