The motion of a particle is defined by the relation x=t 3 -6t 2 -36t-40, where x
ID: 1817110 • Letter: T
Question
The motion of a particle is defined by the relation x=t3-6t2-36t-40, where x and t are expressed in feet and seconds, respectively. Determine:
a)when the velocity is zero
b)the velocity, the acceleration, and the total distance traveled when x=0.
Explanation / Answer
To find velocity you are going to take the derivative of the distance function so since you have: x= t^3-6t^2-36t-40 v= 3t^2 -12t-36 So now just set it equal to 0 and solve: 0 = 3t^2 -12t-36 You can factor out a 3 0 = 3(t^2 -4t-12) ====> Now divide both sides by 3 0 = t^2 -4t-12 You can factor 0 = (t-6)(t+2) Solving for 0 you get 2 answers t = 6s and t = -2s, but since you know you can't have a negative time you have velocity equal to zero at 6s. For the second part I'm going to assume you meant at t=0 or else it wouldn't make much sense. First to find your acceleration function take the derivative of the velocity function so you have: a = 6t-12 Now just plug in 0 wherever you have a t and you will have your answers. Hope this helps.