# NCERT Solutions Class 11 Physics Chapter 3 Motion In A Straight Line

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## Concept Chapter 3 Class 11 Physics Motion In A Straight Line Ncert Solutions

Rectilinear motion

Motion of objects along a straight line is known as rectilinear motion.

Reference point

The point of intersection of three mutually perpendicular axes, labelled as X, Y, and Z axes is called origin (O) and serves as the reference point.

Frame of reference

The coordinates (x, y. z) of an object along with a clock in a system constitutes a frame of reference.

Path length

Path length is a scalar quantity. Total distance covered by object is known as path length.

Displacement

Displacement is a vector quantity. The difference between final and initial position is known as displacement. The magnitude of displacement cannot more than path length.

Let x1 and x2 be the positions of an object at time t1 and t2.

Then its displacement, Δx = x2– x1

If x2> x1, Δx is positive; and if x2< x1,Δx is negative.

Average velocity

Average velocity is defined as the change in position or displacement (Δx) ided by the time intervals (Δt).it is a vector quantity.

$\overline v = \frac{{{x_2} - {x_1}}}{{{t_2} - {t_1}}} = \frac{{\Delta x}}{{\Delta t}}$

Where x1 and x2 be the positions of an object at time t1 and t2.

The SI unit for velocity is m/s or m s–1

Average speed

Average speed is defined as the total path length travelled by object ided by the total time interval during which the motion has taken place. it is a scalar quantity.

${\rm{Average}}\;{\rm{speed = }}\frac{{{\rm{Total}}\;{\rm{path}}\;{\rm{length}}}}{{{\rm{Total}}\;{\rm{time}}\;{\rm{interval}}}}$

The SI unit for speed is m/s or m s–1

Instantaneous velocity

Velocity of an object at a particular instant is known as instantaneous velocity of that instant. In Instantaneous velocity Δt becomes infinitesimally small.

Instantaneous velocity,${v_{ins}} = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta x} \over {\Delta t}} = {{dx} \over {dt}}$ .

Instantaneous velocity is the rate of change of position with respect to time, at that instant.

For uniform motion, Instantaneous velocity is the same as the average velocity at all instants.

Average acceleration

The average acceleration aavg over a time interval is defined as the change of velocity ided by the time interval

$$\overline a = {{{v_2} - {v_1}} \over {{t_2} - {t_1}}} = {{\Delta v} \over {\Delta t}}$$

Where v1 and v2 be the velocity of an object at time t1 and t2.

It is vector quantity.

Instantaneous acceleration

Acceleration of an object at a particular instant is known as instantaneous acceleration of that instant. In Instantaneous acceleration Δt becomes infinitesimally small.

Instantaneous acceleration,${a_{ins}} = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta v} \over {\Delta t}} = {{dv} \over {dt}}$ .

Instantaneous acceleration is the rate of change of velocity with respect to time, at that instant.

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