Linear Motion Revision

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1. There are various equations of motion that can be used to find the velocity (initial or final), displacement, acceleration, or time of travel

$a=\frac{v-u}{t}$

$v_{av}=\frac{v+u}{2}$

$s=ut+\frac{1}{2}a{t}^2$

$v^2=u^2+2as$

$v_{av}=\frac{s}{t}$

2. ‘Uniform motion’ means zero or constant acceleration

   1. When using these equations, directions must be included by using positive values of u, v, a and s as required
   2. The common conventions for directions arre
      1. up is positive, down is negative
      2. right is positive, left is negative
      3. acceleration due to gravity ($9.8m{s}^{-}1$) is negative

3. Drawing diagrams for vertical (up and down) motion

   • Example: a ball is thrown upwards from the top of a building
   • 

4. When using the equation, $s=ut+\frac{1}{2}a{t}^2$, $t$ can be found using the quadratic equation

   1. First convert the equation into the form $A{x}^2+Bx+C=0$
   2. Then, $x=\frac{-B\pm \sqrt{B^2-4AC}}{2A}$
   3. That is, rearrange $s=ut+\frac{1}{2}a{t}^2$ into $(\frac{1}{2}a)t^2+(u)t+(-s)$
   4. $A=\frac{1}{2}a$, $B=u$, $C=-s$
   5. When using the equation $s=ut+\frac{1}{2}a{t}^2$, it is possible to obtain 2 values for $t$ (time). If one of these values is negative, it is ignored. If both values are positive, one is for the upward motion, the other for downward. The body will pass that height going up and coming down