When an object moves or travels in a straight line, it is called Linear Motion or One-Dimensional Motion. This kind of motion doesn’t effected by any other external force. Uniform linear motion is the rate of change of position is constant with respect to time. Some examples of linear motion in daily life can be seen in parade of the soldiers, car moving at constant speed, a bullet targeted from the pistol etc.
Numerical Examples Based on Linear Motion:A man walks on a straight road from his home to a market 3km away with a speed of 6 km/h. The market was closed; he instantly turns and walks back with a speed of 9km/h. What is thea) magnitude of average velocity andb) average speed of the mani) 0 to 30 minii) 0 to 50 miniii) 0 to 40 min?Answer: Time taken by man to go from his home to the market,T1="distance/" speed= 3 km / 6kmh-1= ½ h= 30 minTime taken by man to go from market to home,T2="3km" / 9kmh-1= 1/3 h= 20 minTotal time taken="T1" + T2= ½ + 1/3= 5/6h= 50 mini) 0 to 30 mina) Average Velocity="displacement/" time= 3km/ (1/2) h= 6km/h
b) Average Speed = path length/ time= 3km / (1/2) h= 6km/hii) 0 to 50 minTotal path length covered="3+3"= 6kmTotal displacement = Zeroa) Average Velocity = displacement/ time= 0/ (5/6) h= 0b) Average Speed = total path length/ time= 6km/ (5/6h)= 7.2 kmh-1i) 0 to 40 minDistance moved in 30 min (from home to market) =3kmDistance moved in 10min (from market to home) with speed 9km/h= 9 * 1/6= 1.5km
So, Displacement =3-1.5km=1.5kmTotal path length covered = 3+1.5km= 4.5kma) Average Velocity = 1.5 km/ (40/60)h= 2.25km/hb) Average Speed="4.5" km/ (40/60)h= 6.75km/hLinear Motion Example : SummaryIn such a motion, the object moves along a straight line or a well defined path. Therefore, one- dimensional motion is sometimes known as rectilinear motion or linear motion. Some examples are motion of a train on straight railway track, object dropped from certain height etc.