1. Home
  2. >Physics
  3. >Scalars, Vectors and Motion
Help

Scalars, vectors, and one dimensional motion

All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

Instant and Unlimited Help

24/7 access to the best tips, walkthroughs, and practice questions.

0/2
?
Intros
Lessons
  1. Introduction to scalars, vectors, and one dimensional motion
  2. How to write scalars and vectors; definitions of distance, position and displacement
  3. Definitions of speed and velocity
0/2
?
Examples
Lessons
  1. Distance and displacement, speed and velocity
    Betty walks 5 m to the east, then 7 m to the west, in 10 s.
    1. What is the total distance travelled?
    2. What are Betty's initial and final positions, and displacement?
    3. What is Betty's speed?
    4. What is Betty's velocity?
    1. Rearranging v⃗=Δd⃗/t\vec{v} = \Delta\vec{d}/t for displacement and time
      A car travels at 11.0 m/s [E]
      1. What is its displacement if it travels for 13.5 s?
      2. How long does it take to travel 542 m?
      Topic Notes
      ?

      In this lesson, we will learn:

      • Definition of scalar and vector
      • How to write scalars and vectors in physics
      • The definitions of distance, displacement, speed, and velocity
      • Calculations involving scalars and vectors

      Notes:

      • Scaler: a quantity with a magnitude only

      • Vector:a quantity with magnitude and direction

      • Symbols for vectors can be written with arrows on top (like d⃗\vec{d}), symbols for scalars do not have arrows (like t)
      • Distance, speed, time, and mass are examples of scalars: they do not have a direction.
      • Position, displacement, and velocity are examples of vectors: they do have direction.

      Displacement

      Δd⃗\Delta \vec{d}: d⃗f−d⃗i\vec{d}_f - \vec{d}_i

      Δd⃗:displacement,  in  meters  (m)\Delta \vec{d}: \mathrm{displacement, \;in\;meters\;(m)}

      d⃗f:final  position,  in  meters  (m)\vec{d}_f: \mathrm{final\;position, \;in\;meters\;(m)}

      d⃗i:initial  position,  in  meters  (m)\vec{d}_i: \mathrm{initial\;position,\;in\;meters\;(m)}


      Speed

      v=d/tv = d/t

      v:speed,  in  meters  per  second  (m/s)v:\mathrm{speed, \;in \;meters \;per \;second \;(m/s)}

      d:distance,  in  meters  (m)d:\mathrm{distance, \;in \;meters \;(m)}

      t:time  interval,  in  seconds  (s)t:\mathrm{time \;interval, \;in \;seconds \;(s)}


      Velocity

      v⃗=Δd⃗/t\vec{v} = \Delta \vec{d}/t

      v⃗:velocity,  in  meters  per  second  (m/s)\vec{v}: \mathrm{velocity,\;in\;meters\;per\;second\;(m/s)}