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Study Guide for 1 Dimensional Motion

The exam is primarily based on the content from Chapter 2 of Tipler Physics for Scientists and Engineers and Chapter 2 of Randall Knight Physics for Scientists and Engineers

The format of the exam will be as follows: 5 Open Ended Questions (Not AP Style), 8 Multiple Choice Questions, and 2 Free Response Questions (AP Style)

Sample Open Ended Questions

1. What is the difference between speed and velocity?2. What is the difference between distance and displacement?3. What does the slope of a d-t graph represent?4. What does the slope of a v-t graph represent?5. What does the area under a v-t curve represent?6. What does the area under an a-t curve represent?7. Under which circumstances does an object’s motion satisfy the equation v=(v i+vf)/2?8. How does the average velocity differ from the instantaneous velocity?9. How does the average acceleration differ from the instantaneous acceleration?10. What kinematics equation would you use to solve for the acceleration of an object over an

unknown time interval when you know the distance it has traveled, its initial velocity, and its final velocity? (Write the equation)

11. What kinematics equation would you use to solve for the distance an object has traveled over a known interval of time, acceleration, and initial velocity? (Write the equation)

12. How would you determine an object’s velocity function from its position function? (Write the equation)

13. How would you determine an object’s acceleration function from its velocity function? (Write the equation)

14. How would you determine an object’s velocity function from its acceleration function? (Write the equation)

15. How would you determine an object’s position function from its velocity function?(Write the equation)

16. What is the approximate acceleration due to gravity on earth?

Sample Multiple Choice Questions from AP Physics C Review Books

Sample Free Response Questions from AP Physics C Review Books

2. Consider a particle moving according to the velocity function, v(t) = 8t2-4t + 3. At t= 2s, the position is 25 m.

a) Derive an expression for the position function.

b) Derive an expression for the acceleration function.

c) Determine the average acceleration over the interval t = 1s to t=3s.

d) Find the acceleration at t=2s.

Answers

Multiple Choice

1. E 2. C (Examine Area Under Curve) 3. E 4. C 5. A

6. D (Use y=vit +1/2at2…-25=20t +(0.5)(-10)t2 and solve for t)

7. B

8. D (v(t) =dy/dt=6t2-4…a(t) = dv/dt = 12t…a(3) = 12(3) = 36 m/s2)

9. B (v(t) =∫adt=∫(3t2)dt=t3+10…… v(2) =23+10=18)

10. C (v(t) =dx/dt = (5/2)t3/2… v2~t3 )

Free Response

1a. The speed begins to slow down

1b. The average speed is 10 m/s over both intervals

V=x/t

For 0-1s, V=10 m/ 1s = 10 m/s….. For 1-5s, v=x/t=40m/4s = 10 m/s

1c. For 0-5s, x=A=1/2 bh= ½(5s)(20 m/s) = 50 m

For 5-7s, x = A=1/2bh=1/2(2s)(-10m/s) = -10 m

Adding both, we get 40 m

1d. The acceleration from 0-1s, a=∆v/t=(vf-vi)/t=(20-0)/1 = 20m/s2

The acceleration from 1-7s, a = ∆v/t=(vf-vi)/t = (-10-20)/6= -5m/s2

1e. We keep track of positions vs time

X(m) T(s)0 010 150 540 7

2.

a) x(t) = ∫vdt=∫(8t2-4t+3)dt = (8/3)t3-2t2+3t+C

x(2)=25= (8/3)23-2(2)2+3(2)+C so C =17/3

x(t) =(8/3)t3-2t2+3t+17/3

b)a(t) =dv/dt = 16t -4

c) a = ∆v/t=(vf-vi)/t=(v(3)-v(1))/2

v(3)= 8(3)2-4(3)+3=63 m/s

v(1)=8(1)3-4(1)+3=7m/s

a=(63-7)/2 = 28m/s2

d) a(2)= 16(2) -4 = 28 m/s2