Units and Measurement
Vectors
Motion along a Straight Line
2D Motion
100
What is the difference between precision and accuracy?
Accuracy reflects how close a measurement is to a known or accepted value, while precision reflects how reproducible measurements are, even if they are far from the accepted value
100
A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use a graphical method to find his net displacement vector.
134 km, 80 deg North of East
100
Sketch the velocity-versus-time graph from the following position-versus-time graph.
100
The position of a particle is r(t) = (3.0t^2i + 5.0j − 6.0tk) m.
(a) Determine its velocity and acceleration as functions of time.
(b) What are its velocity and acceleration at time t = 0?
(a): v(t) = (6.0ti + 0j + 6.0k) m/s, a(t) = (6.0i + 0j + 0k) m/s^2
(b): v(0) = 6.0k m/s, a(0) = 6.0i m/s^2
200
The volume of Earth is on the order of 10^21 m^3. What is it in cubic miles (mi^3)?
2.4 * 10^11 mi
200
You drive 7.50 km in a straight line in a direction 15° east of north. (a) Find the distances you would have to drive straight east and then straight north to arrive at the same point.
a. 1.94 km, 7.24 km
200
A particle moves along the x-axis according to x(t)=10t−2t^2 m. (a) What is the instantaneous velocity at t = 2 s and t = 3 s? (b) What is the instantaneous speed at these times? (c) What is the average velocity between t = 2 s and t = 3 s?
(a): v(t)=(10−4t) m/s; v(2s) = 2 m/s, v(3s) = −2 m/s
(b): |v(2s)| = 2m/s, |v(3s)| = 2m/s
(c): v_avg = 0m/s
200
A bullet is shot horizontally from shoulder height (1.5 m) with an initial speed 200 m/s.
(a) How much time elapses before the bullet hits the ground?
(b) How far does the bullet travel horizontally?
(a): t=0.55s
(b): x=110m
300
The speed limit on a road in Rutland is 135000 furlongs per fortnight. Given that a furlong is 1/8 mile and a fortnight is 14 days calculate the speed limit in miles per hour.
50 mi/hr
300
Find the angle between <1, 2, 1> and <1, −1, 1>.
pi/2
300
Professional baseball player Nolan Ryan could pitch a baseball at approximately 160.0 km/h. At that average velocity, how long did it take a ball thrown by Ryan to reach home plate, which is 18.4 m from the pitcher’s mound? Compare this with the average reaction time of a human to a visual stimulus, which is 0.25 s.
t = 2.4 s
9.7x human reaction time
300
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
13.3 m short
400
The acceleration due to gravity on Planet 51 is 7000.2 ft/min^2. Convert this quantity into SI units.
.58924 m/s^2
400
For vectors B =−i − 4j and A =−3i −2j, calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.
(a): A + B = −4i − 6j, |A + B| = 7.211 , θ = 236°
(b): A − B = –2i + 2j, |A − B| = 2.83 , θ = 135°
400
The Shanghai maglev train connects Longyang Road to Pudong International Airport, a distance of 30 km. The journey takes 8 minutes on average. What is the maglev train’s average velocity?
v = 62.5 m/s
400
At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. When she lands, where will she find the ball? Ignore air resistance.
−100m = (−2.0m/s)t − (4.9m/s^2) t^2, t=4.3s, ,x=86.0m
500
Tectonic plates are large segments of Earth’s crust that move slowly. Suppose one such plate has an average speed of 4.0 cm/yr. (a) What distance does it move in 1.0 s at this speed? (b) What is its speed in kilometers per million years?
a): 1.3 *10^-9 m
b): 40 km/(million yrs)
500
A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be expressed in the Cartesian coordinate system as vector F = (−2980.0i + 8200.0j )N, where i and j denote directions to the east and north, respectively. Find the magnitude and direction of the pull.
8724 N, 70 deg North of West
500
The position of a particle moving along the x-axis varies with time according to x(t) = 5.0t^2 − 4.0t^3 m. Find:
(a) the velocity and acceleration of the particle as functions of time.
(b) the velocity and acceleration at t = 2.0 s.
(c) the time at which the position is a maximum.
(d) the time at which the velocity is zero.
(e) the maximum position.
(a): v(t) = 10t − 12t^2 m/s, a(t) = 10 − 24t m/s^2
(b): v(2s) = −28 m/s , a(2s) = −38m/s^2
(c): t = 10.0/12.0 = 0.83 s, which gives x = 1.16 m.
(d): @ t = 0.83 s ; x = 1.16 m
500
A Formula One race car is traveling at 89.0 m/s along a straight track enters a turn on the race track with radius of curvature of 200.0 m. What centripetal acceleration must the car have to stay on the track?
39.6 m/s^2