3.4.1.3
The four SUVAT equations describe motion under constant acceleration
Motion Along a Straight Line — AQA A-Level Physics
- s = displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). (m), u = initial velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. (m s^-1), v = final velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. (m s^-1), a = accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². (m s^-2), $t = time (s)$.
- All variables except time are vectors -- they can be positive or negative.
- SUVAT only applies when accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². is constant.
- 'Starts from rest' means u = 0. 'Falling under gravity' means $a = g = 9.81 m s^-2$.
- Choose positive direction and apply it consistently to all vector quantities.
$$v = u + at$$
- $v$: final velocity (m s⁻¹)
- $u$: initial velocity (m s⁻¹)
- $a$: accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². (m s⁻²)
- $t$: time (s)
$$s = ut + \frac{1}{2}at^2$$
- $s$: displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). (m)
- $u$: initial velocity (m s⁻¹)
- $a$: acceleration (m s⁻²)
- $t$: time (s)
$$s = \frac{(v + u)}{2} t$$
- $s$: displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). (m)
- $v$: final velocity (m s⁻¹)
- $u$: initial velocity (m s⁻¹)
- $t$: time (s)
$$v^2 = u^2 + 2as$$
- $v$: final velocity (m s⁻¹)
- $u$: initial velocity (m s⁻¹)
- $a$: acceleration (m s⁻²)
- $s$: displacement (m)
Worked Example
A train travelling at 50 m s^-1 must decelerate uniformly to 10 m s^-1 in 20 s. How far apart should markers 1 and 2 be placed?
Show Solution
1
List known values
- $u = 50$ m s$^{-1}$
- $v = 10$ m s$^{-1}$
- $t = 20$ s
- $s = ?$
2
Choose the equation with s, u, v, t
$$s = \frac{(u + v)}{2} t$$
3
Substitute and calculate
$$s = \frac{(50 + 10)}{2} \times 20 = 30 \times 20 = 600 \text{ m}$$
Answer
$s = 600$ m
Examiner Tips and Tricks
- This is the most examined part of mechanics.
- Step 1: write out s, u, v, a, t and identify what you know and what you need.
- Step 2: pick the equation that contains those four quantities.
- Step 3: substitute and solve.