Linear motion refers to motion along a straight line. In our daily lives, objects move in various manners—some remain stationary at rest, some move at a steady pace, while others speed up or slow down. To describe linear motion precisely, physics uses specific measurable quantities: distance, displacement, speed, velocity, and acceleration. These quantities can be investigated experimentally using tools like a ticker timer or a photogate system, and mathematically analysed using four linear motion equations under uniform acceleration.
Identify at a glance whether an object is undergoing uniform velocity, uniform acceleration, or uniform deceleration based on ticker tape dot spacing and chart strip heights.
Linear motion deals with objects moving along a straight path. A body's travel can be evaluated through scalars or vectors.
Linear motion is motion in a straight line. An object is said to be at rest when its position remains unchanged with time, such as a taxi waiting in a parking lot.
Distance is the total length of the route covered by an object. Displacement is the shortest distance between the initial position and the final position in a specific direction.
Speed is the rate of change of distance travelled. Velocity is the rate of change of displacement.
Acceleration is the rate of change of velocity. Deceleration occurs when acceleration acts in the opposite direction to the motion of the object.
Speed
Scalar quantity.
Example: An object that travels \(60\ \mathrm{m}\) in \(12\ \mathrm{s}\) has a speed of \(v = \dfrac{60}{12} = 5\ \mathrm{m\,s^{-1}}\).
Velocity
Vector quantity with magnitude and direction.
Acceleration
Vector quantity. The sign of acceleration depends on the chosen positive direction. An object slows down when its acceleration is opposite to its velocity; negative acceleration does not always mean deceleration.
A ticker timer operates on an alternating current power supply with a frequency of \(50\ \mathrm{Hz}\). It makes \(50\) ticks in \(1\) second on ticker tape. One tick is the time interval between two adjacent dots: \(1\ \text{tick} = \dfrac{1}{50}\ \mathrm{s} = 0.02\ \mathrm{s}\). Therefore, \(5\ \text{ticks} = 0.10\ \mathrm{s}\) and \(10\ \text{ticks} = 0.20\ \mathrm{s}\).
For a strip covering displacement \(\Delta s\) in a fixed interval \(\Delta t\), its average velocity is \(v = \dfrac{\Delta s}{\Delta t}\). For example, a 5-tick strip from a \(50\ \mathrm{Hz}\) timer represents \(0.10\ \mathrm{s}\). If its length is \(4.0\ \mathrm{cm} = 0.040\ \mathrm{m}\), then \(v = \dfrac{0.040}{0.10} = 0.40\ \mathrm{m\,s^{-1}}\).
Acceleration is the change in velocity per unit time. If the next 5-tick strip is \(6.0\ \mathrm{cm}\), its velocity is \(0.60\ \mathrm{m\,s^{-1}}\). The average velocities of adjacent strips are separated by \(0.10\ \mathrm{s}\), so \(a = \dfrac{0.60 - 0.40}{0.10} = 2.0\ \mathrm{m\,s^{-2}}\).
A photogate system consists of an electronic timer connected to photogates placed along a runway. It is more accurate because no ticker tape is attached to the trolley, eliminating friction, and it measures time to an accuracy of \(0.001\ \mathrm{s}\), compared to \(0.02\ \mathrm{s}\) for a ticker timer.
Four Linear Motion Equations for Uniform Acceleration
Where \(s\) = displacement, \(u\) = initial velocity, \(v\) = final velocity, \(a\) = acceleration, and \(t\) = time.
Basic derivation: From \(a = \dfrac{v-u}{t}\), rearranging gives \(v = u + at\). Under uniform acceleration, average velocity is \(\dfrac{u+v}{2}\), so \(s = \dfrac{1}{2}(u+v)t\). Substituting \(v = u+at\) gives \(s = ut + \dfrac{1}{2}at^2\). Using \(t = \dfrac{v-u}{a}\) in \(s = \dfrac{1}{2}(u+v)t\) gives \(2as = (u+v)(v-u) = v^2-u^2\), hence \(v^2 = u^2 + 2as\).
Answer in your mind, then press “Check Answer”.
A car travels \(100\ \mathrm{m}\) due East and then reverses \(20\ \mathrm{m}\) due West along the same straight line within \(20\ \mathrm{s}\). What are its total distance and its velocity?
What is the duration of 5 ticks on a ticker tape produced by a \(50\ \mathrm{Hz}\) ticker timer?
A bicycle traveling at \(8\ \mathrm{m\,s^{-1}}\) stops completely over a distance of \(2\ \mathrm{m}\). What is its acceleration?
A negative acceleration value always means the vehicle is moving backwards.
A negative acceleration value means the acceleration points in the chosen negative direction. The object slows down only when acceleration and velocity are in opposite directions; if both are negative, its speed increases.
Distance and displacement are always equal in magnitude.
Distance and displacement have the same magnitude only when an object moves in a straight line without reversing direction. If the path curves or doubles back, distance is strictly greater than displacement.
A ticker timer operating at \(50\ \mathrm{Hz}\) produces \(1\ \text{tick}\) every \(0.50\ \mathrm{s}\).
A frequency of \(50\ \mathrm{Hz}\) means 50 ticks are made per second, so each single tick takes \(T = \dfrac{1}{50}\ \mathrm{s} = 0.02\ \mathrm{s}\).
Objective: Test your understanding of linear motion, ticker timer analysis, and kinematic equations.
1 Why is the measurement of motion using a photogate system and electronic timer more accurate than using a ticker timer?
2 A sports car moving along a straight track accelerates uniformly from \(40\ \mathrm{m\,s^{-1}}\) to \(50\ \mathrm{m\,s^{-1}}\) in \(3\ \mathrm{s}\). What is its displacement during this time?
3 The time interval between two adjacent dots on a ticker tape produced by a \(50\ \mathrm{Hz}\) ticker timer is called one tick, which equals s.
4 When an object moves along a straight road and reduces its velocity over time, it experiences in the opposite direction to its motion.
Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.
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