1. A particle moves along a 1-dimensional line. Itsydisplacement from the origin
ID: 2889307 • Letter: 1
Question
1. A particle moves along a 1-dimensional line. Itsydisplacement from the origin (positive to the right, negative to the left) is s t3 122+36t, t0, where s is measured in meters and t is in seconds. (a) (1 pt) Find the velocity at time t. (b) (1 pt) what is the velocity at time t 3 seconds? (c) (1 pt) When is the particle at rest? (d) (1 pt) When is the particle moving in the positive direction? (e) (2 pts) Find the total distance traveled during the first 8 s (f) (1 pt) Find the acceleration at time t = 3 seconds 2. (a) (5 pts) Find equations of both lines through the point (2,-3) that are tangent to the parabola (b) (2 pts) Show that there is no line through the point (2,7) that is tangent to the parabola. Then sketch a graph to see whyExplanation / Answer
s=t3-12t2+36t
a. velocity, s '(t)= 3t2-24t +36 m/s
b. V(3) = 3(9) -24(3) +36 = -9m/sec
c. s=0
t(t2-12t+36) =0
t=0, (t-6)2=0
t=0, t=6s
d.v(t)>0
3t2-24t +36>0
[0,2)U(6,infinity)
e. s(8)= 83-12(82)+36(8)=32m
f.a (t) = v'(t)=6t-24m/sec2
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