Physics 114A
Introduction to Mechanics
(without calculus)
A course about learning basic physics concepts and applying them
to solve real-world, quantitative, mechanical problems
Lecture 4
Equations of Motion in 1-D
January 11, 2008
Lecturer: Prof. Paul Boynton
Last Time: 1-D Equations of motion
For a = constant:
v(t) = v0 + at
x(t) = x0 + v0t + (a/2)t2
v2 = v02 + 2a(x - x0)
If motion begins from
rest (v0 = 0) and choose
x0 = 0, then:
v(t) = at
x(t) = (a/2)t2
v2 = 2ax
If v = constant (a = 0):
x(t) = x0 + v0t
These expressions provide a complete representation
of motion with constant acceleration
Problem 50
Headline: A Meteorite Strikes. On October 9, 1992, a 27pound meteorite struck a car in Peekskill, NY, leaving a dent
22 cm deep in the trunk. Assume the meteorite struck the car
with a speed of 130 m/s.
What was the magnitude of the meteorite’s deceleration,
assuming it to be constant?
Picture the Problem: The meteorite accelerates from a high
speed to rest upon impacting the car.
Strategy: Employ the relationship between acceleration,
displacement, and velocity (equation 2-12 in your text) to
find the acceleration.
Solution: Solve equation 2-12 for the magnitude of the
acceleration
2
a=
2
0
v !v
2 "x
2
(
)
2 (0.22 m )
0 ! 130 m/s
=
2
= 3.8 #104 m/s 2 ! 4000g
Insight: The high stiffness of steel is responsible for the
tremendous (negative) acceleration of the meteorite.
Problem 59 (yes, 1.1 s, not 1.1 m. I was confused.)
The Infamous Iguana is dashing toward home plate
with a speed of 5.8 m/s when he decides to hit
the dirt. The iguana slides for 1.1 s, just reaching
the plate as he stops (safe, of course).
(a) What is the magnitude and direction of the
iguana’s acceleration?
(b) How far did the iguana slide?
The Infamous Iguana
Picture the Problem: Infamous Iguana slides along a straight line
and comes to rest.
Strategy: Since the initial and final velocities and the time elapsed
are known, the acceleration can be determined from the constant
acceleration equation of motion (equation 2-7). The distance traveled
can be found from the average velocity and the time elapsed
(equation 2-10).
Solution: 1. (a) Solve equation 2-7 for acceleration:
a=
v ! v0 0 ! 5.8 m/s
=
= !5.3 m/s 2
t
1.1 s
where the negative sign means opposite to the direction of motion
(i.e. toward third base).
2. (b) Evaluate equation 2-10 directly:
!x =
1
2
(v + v ) t = (0 + 5.8 m/s) (1.1 s) = 3.2 m
0
1
2
Insight: If dirt had decelerated the iguana at a lesser rate, he would
have a nonzero speed upon crossing home plate. A larger
deceleration would stop the Infamous Iguana before reaching the
plate, and he would have been called out.
This, of course, would be inconceivable!