One-Dimensional Kinematics
1. Which of the following statements about velocity and/or speed are TRUE? List all that apply.
1. Which of the following statements about velocity and/or speed are TRUE? List all that apply.
a. Velocity is a vector quantity and speed is a scalar quantity.
b. Both speed and velocity refer to how fast an object is moving.
c. Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X.
d. The velocity of an object refers to the rate at which the object's position changes.
e. For any given motion, it is possible that an object could move very fast yet have an abnormally small velocity.
f. The phrase "30 mi/hr, west" likely refers to a scalar quantity.
g. The average velocity of an object on a round-trip journey would be 0.
h. The direction of the velocity vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.
| Answer: ADEG a. TRUE - Yes! Speed is a scalar and velocity is the vector. Know this one! b. FALSE - Speed refers to how fast an object is moving; but velocity refers to the rate at which one's motion puts an object away from its original position. A person can move very fast (and thus have a large speed); but if every other step leads in opposite directions, then that person would not have a large velocity. c. FALSE - Person Y has one-half the speed of Person X. If person Y requires twice the time to do the same distance, then person Y is moving half as fast. d. TRUE - Yes! That is exactly the definition of velocity - the rate at which velocity changes. e. TRUE - An Indy Race car driver is a good example of this. Such a driver is obviously moving very fast but by the end of the race the average velocity is essentially 0 m/s. f. FALSE - The presence of the direction "west" in this expression rules it out as a speed expression. Speed is a scalar quantity and direction is not a part of it. g. TRUE - For a round trip journey, there is no ultimate change in position. As such, the average velocity is 0 m/t seconds. Regardless of the time, the average velocity will be 0 m/s. h. FALSE - The direction of the velocity vector depends only upon the direction that the object is moving. A westward moving object has a westward velocity. |
2. A fullback is running down the football field in a straight line. He starts at the 0-yard line at 0 seconds. At 1 second, he is on the 10-yard line; at 2 seconds, he is on the 20-yard line; at 3 seconds, he is on the 30-yard line; and at 4 seconds, he is on the 40-yard line. This is evidence that
a. he is accelerating
b. he is covering a greater distance in each consecutive second.
c. he is moving with a constant speed (on average).
| Answer: C The fullback is moving 10 yards every second. He has a constant speed and thus covers the same distance (10 yd) in each consecutive second. He is not accelerating. |
3. Which one of the following statements is NOT true of a free-falling object? An object in a state of free fall ____.
a. falls with a constant speed of -10 m/s.
b. falls with a acceleration of -10 m/s/s.
c. falls under the sole influence of gravity.
d. falls with downward acceleration which has a constant magnitude.
| Answer: A A free-falling object is an object upon which the only force is gravity. As it falls, it accelerates at a rate of approx. 10 m/s/s. This acceleration value is constant during the entire trajectory of the motion. Since this is the case, the speed can not be constant. |
EXERCISE
Question 1
An airplane accelerate down a runaway at 3.20 m/s/s for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.
a = 3.2 m/s/s t = 32.8 s Vi = 0m/s d =??
d = Vi(t) + 0.5 at^2
d = (0)(32.8) + (3.2)(32.8)^2
d = 1720 m.
Question 2
A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car?
d = 110 m t = 5.21 s Vi = 0 m/s a = ??
d = Vi(t) + 0.5 at^2
110 = (0)(5.21) + 0.5 (a)(5.21)^2
110 = (13.57)a
a = (110)/(13.57)s/s
a = 8.10 m/s/s
Question 3
Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far wil he fall?
a = -9.8
t = 2.6 s
Vi = 0 m/s
d = ??
Vf = ??
d = Vi(t) + 0.5at^2
d = (0)(2.6) + 0.5 (-9.8)(2.6)^2
d = -33 m
Vf = Vi + at
Vf = 0 + (-9.8)(2.6)
Vf = -25.5 m/s
EXAMPLE 1 :
ž A car traveling on a straight road increases its speed from 20 km/h to 100 km/h in 45 s. What is the distance covered by the car?
Solution
ž In this question we have u = 20 km/h, v = 100 km/h and t = 45 s. If we know the magnitude of a, then all the parameters will fit the equation v2 = u2 + 2as.
ž First we have, a = (v – u)/t = (100 – 20) km/h /(45/3600)h
= 6400 km/h-2
ž Thus the distance covered by the car is 0.75 km.
EXAMPLE 2 :
A drag racer starting from rest accelerates in a straight line at a constant rate of 5.5 m/s2 for 6.0 s.
(a) What is the racer’s velocity at the end of this time?
(b) If a parachute deployed at this time causes the racer to slow down uniformly at 2.4 m/s2, how long will the racer take to come to a stop?
Solution,
ž Within the two intervals (before and after parachuted), the final velocity, v1 in the first interval becomes the initial velocity, vo for the second interval.
ž To find the final velocity v1, we use equation
v1 = vo + a1t1 = 0 + (5.5 m/S2)(6.0 s) = 33 m/s
ž For the second interval we use equation
v2 = vo + a2t2 (where vo = v1 = 33 m/s)
 |
EXAMPLE 3:
A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed.
SOLUTION :
| Given:
| Find: a = ?? t = ?? |
vf2 = vi2 + 2*a*d
(88.3 m/s)2 = (0 m/s)2 + 2*(a)*(1365 m)
7797 m2/s2 = (0 m2/s2) + (2730 m)*a
7797 m2/s2 = (2730 m)*a
(7797 m2/s2)/(2730 m) = a
a = 2.86 m/s2
vf = vi + a*t
88.3 m/s = 0 m/s + (2.86 m/s2)*t
(88.3 m/s)/(2.86 m/s2) = t
t = 30. 8 s
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