Please help with these two questions: 1. Consider a particle moving along the x
ID: 2849621 • Letter: P
Question
Please help with these two questions:
1. Consider a particle moving along the x-axis where
x(t)
is the position of the particle at time t,
x'(t)
is its velocity, and
x''(t)
is its acceleration.
x(t) = t3 6t2 + 9t 3, 0 t 10
(a) Find the velocity and acceleration of the particle.
(b) Find the open t-intervals on which the particle is moving to the right. (Enter your answer using interval notation.)
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2.Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration.
A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 7cos(t). At the time t = 0, its position is x = 6.
(a) Find the velocity and position functions for the particle.
(b) Find the values of t for which the particle is at rest. (Use k as an arbitrary non-negative integer.)
t =
(c) Find the velocity of the particle when the acceleration is 0.
Explanation / Answer
1)x(t) = t3 6t2 + 9t 3,
velocity x'(t) = 3*t3-1 6*2t2-1 + 9*1 0
velocity v(t)=x'(t) = 3t2 12t + 9
,, and
acceleration.a(t)=x''(t) = 3*2t 12*1 + 0
acceleration.x''(t) = 6t 12
particle is moving to the right when v(t) > 0
3t2 12t + 9 >0
t2 4t + 3>0
(t-3)(t-1)>0
==>t=(0,1)U(3, 10)