This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. 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) = 13 – 15+2 + 27t – 4, Osts 10 Exercise (a) Find the velocity and acceleration of the particle. Step 1 To obtain the velocity, differentiate v the function x(t) = 13 – 15t2 + 27t – 4with respect to The velocity of the particle is v(t) = x'(t) = t + Submit Skip_(you cannot come back) Exercise (6) Find the open t-intervals on which the particle is moving to the right. Click here to begin! Exercise (c) Find the velocity of the particle when the acceleration is 0. Click here to begin! 15. [1/29 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 5.1.065.MI. SA. MY NOTES This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. 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) = 43 – 15t2 + 27t – 4, Osts 10 Exercise (a) Find the velocity and acceleration of the particle. Click here to begin! Exercise (b) Find the open t-intervals on which the particle is moving to the right. Step 1 The particle is moving to the right when v(t) ? V0. We need to determine when this occurs. In Part (a) we found the velocity of the particle, v(t) = 3+2 – 30t + 27. We must now factor v(t). v(t) = 3t2 - 30t + 27 = 3(t2-1 t + = 3(t - :- 1)(t- By inspection we can see that v(t) is greater than 0 when both (t – 1) > 0 and > 0 or, alternately, when both (t - 1) < 0 and < 0. Recall that we are also given Osts 10. Submit Skip (you cannot come back) 15. [1/29 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 5.1.065.MI. SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. 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) = 13 – 15t2 + 27t – 4, Osts 10 Exercise (a) Find the velocity and acceleration of the particle. Click here to begin! Exercise
(b) Find the open t-intervals on which the particle is moving to the right. Click here to begin! Exercise
(c) Find the velocity of the particle when the acceleration is 0. Step 1 To find the velocity of the particle when the acceleration is o, first obtain the value of time, t, when the acceleration is 0. In Part (a) we found the acceleration of the particle, a(t) = 6(t – 5). We need to set a(t) = and solve for t. 6(t – 5) = t - 5 = t = Submit Skip(you cannot come back)