Motion with constant acceleration review

Key terms

Equations

• $x_0$x, start subscript, 0, end subscript is
  [initial position]
• $x$x is the
  [final position]
• $t$t is the
  [time interval]
• $v_0$v, start subscript, 0, end subscript is initial velocity
• $v$v is final velocity
• $a$a is acceleration

• Acceleration is constant over the time interval

Using the kinematic formulas

Choosing the best kinematic formula

Finding the known variables

Common mistakes and misconceptions

1. People forget that some of the kinematic variables are vectors and can have negative signs. For example, if upward is assumed to be positive, then the acceleration due to gravity must be negative: $a_g=-9.81\dfrac{\text{m}}{\text{s}^2}$a, start subscript, g, end subscript, equals, minus, 9, point, 81, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. A missing negative sign is a very common mistake, so don't forget to check which direction is defined as positive!
2. People forget that the kinematic variables we plug into a kinematic formula must be consistent with that time interval. In other words, the initial velocity $v_0$v, start subscript, 0, end subscript has to be the velocity of the object at the initial position and start of the time interval $t$t. Similarly, the final velocity $v$v must be the velocity at the final position and end of the time interval $t$t.
3. The second kinematic equation, $x=x_0+ v_0 t+\dfrac{1}{2}at^2$x, equals, x, start subscript, 0, end subscript, plus, v, start subscript, 0, end subscript, t, plus, start fraction, 1, divided by, 2, end fraction, a, t, squared, might require using the

   quadratic formula

   .

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