Please explain how to go about finding each these answers. The position of a par
ID: 3188278 • Letter: P
Question
Please explain how to go about finding each these answers.The position of a particle is given by s=t^3-9t^2-3. where t is measured in seconds and s in meters.
a.) Find the velocity at time t.
b.) What is the velocity after 1 sec?
c.) When is the particle at rest?
d.) When is the particle moving in the positive direction? Negative direction?
e.) Draw a diagram representing the motion of the particle.
f.) Find the total distance traveled by the particle during the first 5 sec.
g.) Find the acceleration at time t.
h.) Find the acceleration after 4 sec.
i.) When is the particle speeding up? Slowing down?
Explanation / Answer
1. velocity is the speed. you have the position formula so the slope would tell you the speed. the change in y over the change in x would be how much it has moved in a certain amount of time. which is speed. 2. i think you plug 1 into the derivative 3. particle is at rest when the velocity is 0. so take the derivative and set it equal to 0. 4. positive direction when the derivative is positive ,negative direction when slope is negative. e graph the position function. it where is it at all times. f. integral from 0 to 5 of position function g. acceleration is the 2nd derivative. you would h i think you plug 4 into the 2nd derivative i. speeding up when 2nd derivative is positive, slowing down when its negative.