Lecture 5 : Introduction to Physics PHY101. Chapter 2: Equations of Kinematics for Constant Acceleration in 1 Dim. (2.4, 2.5, 2.7) Free Fall (2.6) Chapter 3: Equations of Kinematics for Constant Acceleration in 2 Dim. (3.1, 3.2). Summary of concepts from last lecture.
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Acceleration in 1 Dim. (2.4, 2.5, 2.7)
Acceleration in 2 Dim. (3.1, 3.2)
1) v>0, a>0
2) v>0, a<0
3) v<0, a>0
4) v<0, a<0
If speed is increasing, v and a are in same direction.
If speed is decreasing, v and a are in opposite direction.
Which of the following statements is most nearly correct?
1 - A car travels around a circular track with constant velocity.
2 - A car travels around a circular track with constant speed.
3- Both statements are equally correct.
On a circular track, the direction that the car is traveling in is always changing, and since velocity takes into account the direction of travel, the velocity is always changing. Speed, however, is independent of direction and so the speed can stay constant.
Consider an object which moves from the initial position x0, at time t0
with velocity v0, with constant acceleration along a straight line.
How does displacement and velocity of this object change with time ?
aav=a = (v-v0) / (t-t0) => v(t) = v0 + a (t-t0) (1)
vav = (x-x0) / (t-t0) = (v+v0)/2 => x = x0 + (t-t0) (v+v0)/2 (2)
Use Eq. (1) to replace v in Eq.(2):
x(t) = x0 + (t-t0) v0 + a/2 (t-t0) 2 (3)
Use Eq. (1) to replace (t-t0) in Eq.(2):
v2 = v02 + 2 a (x-x0 ) (4)
[Chapter 2, problem #15]
t0= 0 s, v= -5.36 m/s, t=3.00 s, aav=-0.640 m/s2
v0 = ? m/s
aav = (v-v0)/(t-t0) => v0= v- aav (t-t0) = -3.44 m/s
v0 = 3.44 m/s due west
1. Before the parachute opens (car moves +x direction):
t0= 0 s, v01 = 0 m/s, x1=+402 m, a1=+17 m/s2
2. After the parachute opens:
t0= 0 s, x2=+3.50 x 102 m, a2=-6.10 m/s2, v=? m/s
v2=v022+2 a2 x2 Get v022 from 1.: v02=(2 a1 x1 )1/2=+117 m/s
=> v2=(v02+2 a 2 x2)1/2=+96.9 m/s
The acceleration due to gravity is always pointing
downward with magnitude g=9.80 m/s2.
A ball is thrown vertically upward. At the very top of its trajectory, which of the following statements is true:
1. velocity is zero and acceleration is zero2. velocity is not zero and acceleration is zero3. velocity is zero and acceleration is not zero4. velocity is not zero and acceleration is not zero
The velocity vector changes from moment to moment, buts its acceleration vector does not change. Though the velocity at the top is zero, the acceleration is still constant because the velocity is changing.
t0= 0 s, v0 = 0 m/s, t=1.2 s, a=-9.80 m/s2
Y1/2=v0 t + ½ a t2 = -7.1 m
2. From rest all the way to the ground, y=2 Y1/2
t0= 0 s, v0 = 0 m/s, a=-9.80 m/s2, t= ? s
Y=v0 t + ½ a t2 = ½ a t2 => t= (2 y/a)1/2=1.7 s
Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground?
1. Dennis' ball2. Carmen's ball3. Same
Consider an object which moves in the (x,y) plane from the initial
position r0, at time t0 with velocity v0, with constant acceleration.
Same concepts as in one dimension !
Equations of kinematics are derived for the x and y components
separately. Same equations as in one dimension !