Motion in a Straight Line
Class 11 Physics · Physics Part I · Chapter 2
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Summary
This chapter describes rectilinear motion — the motion of an object treated as a point along a straight line — without enquiring into its causes (kinematics). Position is measured from a chosen origin and may be positive or negative. Average velocity is displacement divided by time interval, while instantaneous velocity is the limit of average velocity as the interval shrinks to zero, \(v=\mathrm{d}x/\mathrm{d}t\); graphically it is the slope of the tangent to the position-time graph. Speed is the magnitude of velocity, and average speed (path length over time) is always greater than or equal to the magnitude of average velocity. Acceleration is the rate of change of velocity, \(a=\mathrm{d}v/\mathrm{d}t\), and may be positive, negative or zero. The area under a velocity-time graph equals the displacement. For uniformly accelerated motion the three kinematic equations \(v=v_0+at\), \(x=v_0t+\tfrac12 at^{2}\) and \(v^{2}=v_0^{2}+2ax\) relate displacement, time, initial and final velocities and acceleration, and can be derived graphically or by calculus. Free fall under gravity, with \(a=-g\), is an important special case, illustrated by Galileo's law of odd numbers, stopping distance and reaction time. Relative velocity describes the motion of one object as seen from another.
Instantaneous velocity and speedAccelerationKinematic equations for uniformly accelerated motionVelocity-time and position-time graphsFree fall under gravityRelative velocity in one dimension
Key terms
Instantaneous velocity
The limit of average velocity as the time interval tends to zero, \(v=\mathrm{d}x/\mathrm{d}t\); the slope of the position-time tangent.
Average speed
Total path length divided by the time interval; it is greater than or equal to the magnitude of average velocity.
Acceleration
The rate of change of velocity with time, \(a=\mathrm{d}v/\mathrm{d}t\); it can be positive, negative or zero.
Uniform motion
Motion in which equal displacements occur in equal time intervals, so velocity is constant and acceleration is zero.
Free fall
Motion of a body under gravity alone, with constant downward acceleration \(g\approx9.8\ \text{m s}^{-2}\).
Relative velocity
The velocity of one object with respect to another, equal to the difference of their velocities.
Extra questions & answers
Try one from this chapter
Instantaneous velocity is the slope of the: