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**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 x_{1} and x_{2} be the positions of an object at time t_{1 }and t_{2}.

Then its displacement, Δx = x_{2}– x_{1}

If x_{2}> x_{1}, Δx is positive; and if x_{2}< x_{1},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 x_{1} and x_{2} be the positions of an object at time t_{1 }and t_{2}.

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 a_{avg} 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 v_{1} and v_{2} be the velocity of an object at time t_{1 }and t_{2}.

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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