This is the second of the two introductory courses in Physics. It is a calculus based course. The course is examined at two levels, with Higher Physics 1B being the higher of the two levels. While the same content is covered as Physics 1B, Higher Physics 1B features more advanced assessment, including separate tutorial and laboratory
这是一份unsw新南威尔斯大学PHYS1131的成功案例
\begin{prob}
A car started moving from rest with a constant acceleration. At some moment of time, it covered the distance $x$ and reached the speed $v$. Find the acceleration and the time.
Solution. The formulas for the motion with constant acceleration read
$$
v=a t, \quad x=\frac{1}{2} a t^{2},
$$
where we have taken into account that the motion starts from rest (all initial values are zero). If $v$ and $x$ are given, this is a system of two equations with the unknowns $a$ and $t$. This system of equations can be solved in different ways.
For instance, one can express the time from the first equation, $t=v / a$, and substitute it to the second equation,
$$
x=\frac{1}{2} a\left(\frac{v}{a}\right)^{2}=\frac{v^{2}}{2 a} .
$$
From this single equation for $a$ one finds
$$
a=\frac{v^{2}}{2 x}
$$
Also, one can relate $x$ to $v$ as follows
$$
x=\frac{1}{2} a t \times t=\frac{1}{2} v t .
$$
After that one finds
$$
t=\frac{2 x}{v}
$$
and, further,
$$
a=\frac{v}{t}=\frac{v}{2 x / v}=\frac{v^{2}}{2 x}
$$
PHYS1131 COURSE NOTES ：
A missile launched from a cannon with the initial speed $v_{0}$ targets an object at the linear distance $d$ from the cannon and at the height $h$ with respect to the cannon. Investigate the possibility of hitting the object and the targeting angles.
Solution. The formula for the motion of the missile has the form (motion with constant acceleration)
$$
z=v_{0 z} t-\frac{1}{2} g t^{2}, \quad x=v_{0 x} t .
$$
The instance of these general formulas corresponding to hitting the target is
$$
h=v_{0 z} t_{f}-\frac{1}{2} g t_{f}^{2}, \quad d=v_{0 x} t_{f} .
$$
From the first equation one finds $t_{f}$ as in the preceding problem,
$$
t_{f}=\frac{1}{g}\left(v_{0 z} \pm \sqrt{v_{0 z}^{2}-2 g h}\right) .
$$