Motion Along a Straight Line

Displacement, velocity, acceleration, motion graphs, SUVAT equations, drag forces, terminal velocity, and the required practical for determining g.

Spec Points Covered
  • Define displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)., velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. and 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. as vector quantities.
  • Distinguish between instantaneous and average speed/velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
  • Interpret displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).-time, velocity-time and accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻².-time graphs.
  • Derive information from the gradient and area under motion graphs.
  • Select and apply the four SUVAT equations for constant accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻²..
  • Explain drag forces and terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. qualitatively.
  • Describe the required practical for measuring g using free fallMotion under gravity alone, with no other forces acting. All objects in free fall near Earth's surface have the same acceleration, g = 9.81 m s⁻²..
Notes
01 Displacement, velocity and acceleration are the vector forms of distance, speed and time-rate quantities Displacement 3.4.1.3 → 02 Instantaneous velocity is the gradient of a displacement-time graph at a point 3.4.1.3 → 03 Displacement-time graphs: gradient = velocity 3.4.1.3 → 04 Velocity-time graphs: gradient = acceleration, area = displacement 3.4.1.3 → 05 Acceleration-time graphs: area = change in velocity 3.4.1.3 → 06 A bouncing ball has constant acceleration but changing velocity direction 3.4.1.3 → 07 The four SUVAT equations describe motion under constant acceleration $v = u + at$ 3.4.1.3 → 08 Drag forces oppose motion and increase with speed Drag force 3.4.1.3 → 09 Terminal velocity is reached when drag equals weight Terminal velocity 3.4.1.3 → 10 Required practical: measuring g by free fall with light gates 3.4.1.3 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
SUVAT: $v = u + at$
$$v = u + at$$
  • Where:
    • $v$ = final velocity (m s⁻¹)
    • $u$ = initial velocity (m s⁻¹)
    • $a$ = acceleration (m s⁻²)
    • $t$ = time (s)
No displacement required.
Velocity
$$v = \frac{\Delta s}{\Delta t}$$
  • Where:
    • $v$ = velocity (m s⁻¹)
    • $Δs$ = change in displacement (m)
    • $Δt$ = change in time (s)
Average velocity if applied over a finite interval.
SUVAT: $s = ut + 0.5at^2$
$$s = ut + \frac{1}{2}at^2$$
  • Where:
    • $s$ = displacement (m)
    • $u$ = initial velocity (m s⁻¹)
    • $a$ = acceleration (m s⁻²)
    • $t$ = time (s)
No final velocity required.
Acceleration
$$a = \frac{\Delta v}{\Delta t}$$
  • Where:
    • $a$ = acceleration (m s⁻²)
    • $Δv$ = change in velocity (m s⁻¹)
    • $Δt$ = change in time (s)
Average acceleration if applied over a finite interval.
SUVAT: $s = (v+u)t/2$
$$s = \frac{(v + u)}{2} t$$
  • Where:
    • $s$ = displacement (m)
    • $v$ = final velocity (m s⁻¹)
    • $u$ = initial velocity (m s⁻¹)
    • $t$ = time (s)
No acceleration required.
SUVAT: $v^2 = u^2 + 2as$
$$v^2 = u^2 + 2as$$
  • Where:
    • $v$ = final velocity (m s⁻¹)
    • $u$ = initial velocity (m s⁻¹)
    • $a$ = acceleration (m s⁻²)
    • $s$ = displacement (m)
No time required.
Q Retrieval Practice All 12 Questions →
Q1. Define displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)..
The distance of an object from a fixed point in a specified direction.
Q2. What does the gradient of a displacement-time graph represent?
Velocity.
Q3. What does the area under a velocity-time graph represent?
Displacement.
Q4. What does the area under an acceleration-time graph represent?
Change in velocity.
Q5. State the four SUVAT equations.
v = u + at, s = ut + 0.5at^2, s = (v+u)t/2, \(v^{2}\) = \(u^{2}\) + 2as.