SPH4UI Lecture 1 Notes - The Burns Home Page
SPH4UI Lecture 1 Notes - The Burns Home Page
SPH4UI Lecture 1 Notes - The Burns Home Page
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Sample Problem Solution<br />
• Trigonometric solution<br />
From the Law of Cosines,<br />
2 2 2<br />
R P Q 2PQcos<br />
B<br />
2 2<br />
40N 60N 240N60Ncos155<br />
R 97.73N<br />
From the Law of Sines,<br />
sin A sin B<br />
<br />
Q R<br />
Q<br />
sin A<br />
sin B R<br />
60N<br />
sin155<br />
97.73N<br />
A 15.04<br />
20 A<br />
35.04<br />
Motion in 1 dimension<br />
• In 1-D, we usually write position as x(t).<br />
• Since it’s in 1-D, all we need to indicate direction is + or .<br />
Displacement in a time t = t 2 - t 1 is x = x(t 2 ) - x(t 1 ) = x 2 - x 1<br />
x<br />
x<br />
x<br />
x<br />
2<br />
1<br />
t 1 t 2<br />
t<br />
some particle’s trajectory<br />
in 1-D<br />
t<br />
1-D kinematics<br />
1-D kinematics...<br />
• Velocity v is the “rate of change of position”<br />
• Average velocity v av in the time t = t 2 - t 1 is:<br />
x<br />
x<br />
x<br />
x<br />
2<br />
1<br />
x( t2) x( t1)<br />
x<br />
vav<br />
<br />
<br />
t t t<br />
t 1 t 2<br />
t<br />
2 1<br />
trajectory<br />
V av = slope of line connecting x 1 and x 2 .<br />
t<br />
• Consider limit t 1 t 2<br />
• Instantaneous velocity v is defined as:<br />
dx()<br />
t<br />
vt () <br />
dt<br />
so v(t 2 ) = slope of line tangent to path at t 2 .<br />
x<br />
x<br />
x<br />
x<br />
2<br />
1<br />
t 1 t 2<br />
t<br />
t<br />
<strong>Page</strong> 8
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