1. The position of a particle moving along a straight line at any time t is given by s(t)=2t³–4t²+2t–1. What is the acceleration of the particle when t=2?

(A) 32

(B) 16

(C) 4

(D) 8

(E) 0

2. A particle moves along the x-axis so that at any time t is given by x(t)= (t+1) (t–3)³. for what values of t is the velocity of the particle increasing?

(A) t>3 only

(B) 0<t<3 only

(C) 1<t<3 only

(D) t<1 and t>3

(E) 0<t<3 and t>3

such a way that its position at time t is given by x(t)= .What is the acceleration of the particle at time t=0?

(A) ‐3/5

(B) ‐4

(C) 4

(D) 2

(E) ‐2

4. A particle moves along the x-axis so that at any time t its position is given by x(t)= + cos(2t) What is the acceleration of the particle at t= ?

(A) 0

(B) 1/2

(C) 3/2

(D) 5/2

(E) 7/2

5. The position of a particle moving along a straight line at any time t is given by s(t)= t²+4t+4. What is the acceleration of the particle when t=4?

(A) 0

(B) 2

(C) 4

(D) 8

(E) 12

6. A particle moves along the x-axis in such a way that its position at time tis given by x(t)= 3t⁵–25t³+60t. For what values of t is the particle moving to the left?

(A) -2<t<1 only

(B) 1<t<2 only

(C) -1<t<1 and t>2

(D) -2<t<-1 and 1<t<2

(E) t<-2, -1<t<1, and t>2

7. If the position of a particle on the x-axis at time t is -5t², then the average velocity of the particle for 0 t 3 is

(A) -45

(B) -30

(C) -15

(D) -10

(E) -5

8. A particle moves along the x-axis in such a way that its position at time t is given by x(t)=t²–6t+5. For what value of t is the velocity of the particle zero?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

9. The acceleration of a particle moving along the x-axis at time t is given by a(t)= 6t-2. if the velocity is 25 when t=3 and the position is 10 when t=1, then the position x(t)=

(A) 9t²+1

(B) 3t²–2t+4

(C) t³–t²+4t+6

(D) t³–t²+9t–20

(E) 36t³–4t²–77t+55

10. A particle moves along the x-axis so that any time t is greater than or equal to zero its position is given by x(t)= t³–3t²–9t+1. For what values of t is the particle at rest?

(A) No values

(B) 1 only

(C) 3 only

(D) 5 only

(E) 1 and 3

ANSWERS

1. b2. d

3. c4. e

5. b6. b

7. c8. 9

9. c10. c

Problems Worked Out

Links to reach answers to all 10 problems

1-5

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6-10

scan0038.jpg.mu13u05.partial