AP Calculus BC : 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals- Exam Style questions with Answer- MCQ

Question

A particle moves along the x-axis so that its acceleration at any time t is at \(a(t)=2t-7 \) . If the initial velocity of the particle is 6, at what time t during the interval 0 ≤ t ≤ 4 is the particle farthest to the right?

(A) 0                                       (B) 1                                       (C) 2                                            (D) 3                                                (E) 4

Answer/Explanation

Ans:B

 

Question

At t = 0 a particle starts at rest and moves along a line in such a way that at time t its acceleration   is  \(24t^{2}\) feet per second per second. Through how many feet does the particle move during the first 2 seconds?

(A) 32                (B) 48            (C) 64                       (D) 96                        (E) 192

Answer/Explanation

Ans:A

The particle is always moving to the right, so distance 

Question

The acceleration α of a body moving in a straight line is given in terms of time t by α= −8 6t . If the velocity of the body is 25 at t =1 and if ( ) s t is the distance of the body from the origin at time t, what is (4)-s(2)?
(A) 20                                 (B) 24                                             (C) 28                                                (D) 32                                                         (E) 42

Answer/Explanation

Ans:D

Question

 If the velocity of a particle moving along the x-axis is \(v(t )=2t-4\) and if at t = 0 its position is 4, then at any time t its position \((x)t\)  is
(A) \(t^2-4t\)                        (B) \(t^2-4t-4\)                     (C) \(t^2-4t+4\)                  (D) \(2t^2-4t\)                   (E) \(2t^2-4t+4\)

Answer/Explanation

Ans:C

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