LINEAR MOTION
Linear motion means – movement along a straight line
- The following terms are used to describe the movement of an object in a given duration
of time.
(a) Distance (d or s)
- this is the measured length along the path of a moving object
- distance is a scalar
- SI Unit: the metre (m)
(b) Displacement (s)
Displacement is the distance moved in a specific direction
i.e.
Displacement is the direct distance between two points
- Displacement is a Vector.
- SI unit: the metre (m).
Consider an object that moves from point A to point B along a path X.
- the measured length along path X represents distance covered
- the measured length along path Y displacement of the object when it moves from A to
B.
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(c) Speed (𝒗)
- Speed measures how fast or how slow an object is moving with time and is defined as,
Speed is the distance moved per unit time
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑
i.e. 𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝑑
i.e. v =
𝑡
- Speed is a scalar quantity.
- The SI unit for speed is the metres per second (m/s)
- Other units include; km/h, km/s, km/day, etc.
(d) Average Speed (𝒗)
Objects e.g vehicle mostly move with changing speeds and even make stops in
between their journey. An average speed can be calculated for their journey, i.e.,
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝒅
v =
𝒕
from which we can write,
𝒅
𝒅= 𝒗×𝒕 and t =
𝒗
- The SI unit for speed is the metres per second (m/s)
Example
A vehicle covers 200 km in 1.25 hours then stops for 0.25 hours before completing the
remaining 60 km of its journey in 0.5 hours. Calculate in km/h, the average speed of the
vehicle.
Solution
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑 = 200 + 60 = 260 𝑘𝑚
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 = 1.25 + 0.25 + 0.5 = 2.0 ℎ𝑜𝑢𝑟𝑠
260
v =
2
= 130 𝑘𝑚/ℎ
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Distance – Time graphs
Gradient of a Distance – Time graph represents Speed
Gradient also means – Slope or Steepness
(a) For an object moving with constant speed
- Graph has a constant gradient, hence, object moving with constant speed.
The two graphs A and B shown below are of two objects A and B that are
moving with constant speeds but of different sizes.
- both graphs are straight lines with constant gradients representing constant
speeds.
- graph A is steeper than graph B showing that object A has a higher speed than
object B.
(b) For an object that is stationary
- The gradient of the graph is zero, speed of object is zero (object not moving)
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(c) For an object moving back to its starting point
The graph shows object moving back to its starting point
(d) For object moving with increasing speed (accelerating)
- The graph has an increasing gradient showing speed of the object is increasing
(object is accelerating)
(e) For object moving with decreasing speed (decelerating)
- The graph has a reducing gradient showing speed of the object is reducing
(object is decelerating)
Example
Below is a distance – time graph for an object that is moving along a level road at a
constant speed.
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(a) Calculate the speed of the object during the 8 seconds.
(b) What is the speed of the object at time, t = 3.7 seconds
Exercise
How does the graph above show that the object is moving with constant speed?
Exercise
The graph below shows the motion of a boy from his home to a shop then back to
his home.
(a) How far is the shop from the boy’s home?
(b) How long does the boy take to reach the shop?
(c) Calculate the boy’s average speed when going to the shop.
(d) Calculate the boy’s speed in section C of the graph.
(e) How does the graph show that the boy is moving faster in section A than in
section C of the graph?
(f) In which section(s) of the graph is the boy at rest during his journey?
(g) How much time does the boy spend while at rest during his journey?
(h) How long does the entire journey take?
(i) What is the total distance moved by the boy at the end of his journey?
(j) Calculate the boy’s average speed for the entire journey.
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