Test 1 Review

**Physics I Sp 01**

** **

Here is a sampling of problems that I would expect you to be able to solve, or answer.

1) Given 1 km = .62 miles, convert miles/hour to meters/min.

**(miles/hr)(1 km/.62miles)(1000 m/1 km)(1 hr/60 min) =
26.9 m/min**

2) When measuring a rectangle for a class project lazy Goofus only measures to the nearest cm and measures 4 x 5 for an area of 20 sq. cm. Gallant takes his time

and measures to the nearest mm, getting 3.6 x 4.7, and he reports the area as 16.9 sq cm.

Which area measurement is more accurate, and why? Who had points deducted for

having the wrong number of significant figures in his answer, and why?

**Gallant’s answer is more accurate since the measurements
were more precise,**

**however he should have given his answer to two
significant figures, 17 sq cm.**

3) If you read that a star is an order of magnitude of 5 larger than the earth, how many times the size of earth is the star?

**Orders of magnitude are powers of ten. The star is 100000 larger than earth.**

4) Given **A **= 3**i **– 2**j **+ 2**k**, and **B
**= 2**i **+ **j **- 2**k **Find:

a) 2**A + B = (6 + 2)i + (-4 + 1)j + (4 – 2)k = 8i – 3j +2k**

** **

b) _{} **= (3)(2) + (-2)(1)
+ (2)(-2) = 6 – 2 – 4 = 0**

c) _{} **= -6i + 10j +7k**

d) _{} **length of A is _{}, the length of B is **3

e) The angle between **A** and **B **

**Since the dot
product was 0, the vectors must be perpendicular, or 90 degrees.**

** **

5) A man walks 4 miles at 42 degrees N of E, then walks 7 miles 50 degrees W of N. What is the magnitude and direction of his net displacement?

**Let the first vector be A, and the second B. **

** **

**Then, _{}The resultant vector, C = A + B, has components _{}**

**The magnitude of C is 7.6, and it is located 71.6 degrees
N of E.**

6) Describe the difference between translational motion and rotational motion. Why can

an object undergoing translational motion be treated as a “point” object?

**the same motion.
Since every part of the object moves the same, we can collapse**

**the object to one of its “points”. Rotational motion differs since not all the
parts**

**are moving the same.
Some may even be at rest while others rotate around them.**

7) A car travels west for 50 miles at a speed of 70 miles/ hour, then immediately returns

at 60 miles per hour. Find the total distance traveled and displacement of the car. Find

the average speed, and average velocity of the car.

**distance = 50 + 50 = 100 miles, displacement = 0
(returned to same spot)**

** **

**average speed = 64.6 miles/hr (total time = 50/70 + 50/60
= 1.5476 hrs**

** average
velocity = 0**

8) The position of a particle is given by the equation _{}

a)Find the average velocity between t = 1, and t = 3.

b) Find the instantaneous velocity at t = .5

_{} **used the
derivative.**

c) Find the instantaneous acceleration at t = 1

_{} **used the second
derivative**

d) Find the average acceleration between t = 1, and t = 2.

**Now use the first derivative for the velocity function to
find the points (1, -1)**

**and (2, 8) and find the slope = 9/1 = 9 **

9) Consider the velocity (m/s) vs. time (s) graph.

**v**

** **

**10**

**5**

**0 5 10
15**

a) Where is the acceleration positive, zero, negative? **approximately:**

**Using interval notaion: positive (0, 3), zero at t = 3,
negative (3, 18)**

b) Does the particle ever reverse direction? If so, at what time?

c) Estimate the displacement of the particle between 5 and 10 seconds.

**a rectangle and another piece that looks like about half
the rectangle**

**to get 25 + 25/2 = 75/2 sq units.**

d) Estimate the average velocity between 0 and 5 seconds.

**The acceleration is not constant so I cannot find
this. I would need the**

**displacement graph and then find the slope between those
points.**

e) Estimate the average acceleration between 0 and 5 seconds.

**Use the points from (d) and find the slope = (10 – 3)/(5
– 3) = 7/2 m/s/s**

10) A car is initially moving at 112 km/h. Find its acceleration and the time

taken to stop given that:

a) it brakes to a stop in 64m

**initial velocity = 31.1 m/s, final velocity = 0, and change in displacement is**

**64 m. Use _{} to find a = -7.6
m/s/s, and use another**

**kinematics equation (your choice) to find t = 4.1 sec.**

b) it crashes into a wall and crumples in 1 m.

**a =
-483.6 m/s/s t = .06 sec OUCH**