3.1 Motion in a straight line with uniform velocity

  Motion in One Dimension

    1.0 Introduction
    2.0 Kinematic variables
    3.0 Motion in one dimension
    4.0 Derivation of the kinematics equation
    5.0 Vertical motion under gravity
    6.0 Analysis of motion through graph
    7.0 Relative motion
    8.0 Simultaneous motion of two bodies
    9.0 River boat problem
    10.0 Aircraft-wind problem
    11.0 Rain problem

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3.1 Motion in a straight line with uniform velocity

When a particle is moving with uniform velocity, it means its acceleration is zero.

So, displacement in time $t$ is given by,
$$d = vt$$

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Question: A particle travels in a straight line moves half a distance with a constant velocity of $10\ m/s$ and next half distance with a constant velocity of $5\ m/s$. What is the average velocity of the particle during the entire motion?

Solution:

$${t_1} = \frac{d}{{10}}$$and$${t_2} = \frac{d}{5}$$Total time $(T)$ can be calculated as, $$T = {t_1} + {t_2}$$$$T = \frac{d}{{10}} + \frac{d}{5}$$$$T = \frac{{3d}}{{10}}$$Average velocity calculated as, $${v_{avg}} = \frac{{{\text{Total displacement}}}}{{{\text{Total time}}}}$$$${v_{avg}} = \frac{{2d}}{{3d}} \times 10$$$${v_{avg}} = 6.67m/s$$