Speed And Velocity - Practice Questions & MCQ

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Speed and velocity is considered one of the most asked concept.
47 Questions around this concept.

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A particle is moving with velocity $\vec{v}=K(y\hat{i}+x\hat{j}),where\; K$ is a constant. The general equation for its path is

$y^{2}=x^{2}+constant$

$y=x^{2}+constant$

$y^{2}=x+constant$

$xy=constant$

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Concepts Covered - 1

Speed and velocity

I. Speed

Rate of change of distance with time.
Formula-

$Speed = \frac{Change\, in \, distance}{change \, in\, time}$

$v=\frac{distance }{speed}$

Tips of Speed-

S.I. unit $\rightarrow$ $ms^{-1}$ or meters per second.
Dimensions= $LT^{-1}$
Speed is a scalar quantity.

E.g: A body covers a distance of 18m in 1 sec

Using formula of speed . $v= \frac{distance}{time}$ $= \frac{18m}{1s}\Rightarrow 18m/s$

II . Average Speed and Instantaneous Speed

Average Speed-

Amount of total distance covered in total time.
Formula-

$Average\, speed =\frac{total \, distance\, covered}{total \, time\, taken}$ , $v_{av}= \frac{s}{t}$

E.g A body covers a total distance of 50 m with variable speed in 5 sec.

$v_{av}= \frac{s}{t}$

$\Rightarrow \frac{50m}{5s}= 10m/s$

Average Speed = 10 m/s

Tips for average speed-

If an object or body covers s1 distance in t1 time and s2 distance in t2 time then average speed is calculated by the

Formula- $V_{av}= \frac{s_{1}+s_{2}}{t_{1}+t_{2}}$

Instantaneous Speed-

It is speed at that particular instant or small interval of time.
Formula-

$v_{inst}= \lim_{\Delta t\rightarrow 0}\frac{\Delta x}{\Delta t}$

III. Velocity

Rate of change of displacement with time.
Formula-

$V=\frac{displacement}{time}$

Tips For velocity-

S.I. unit $\rightarrow$ m/s
Dimensions- $LT^{-1}$
Velocity is a vector quantity.
Velocity is also called speed in a definite (particular) direction.

IV. Average Velocity and Instantaneous Velocity

Average Velocity-

Amount of total distance covered in total time.
Formula-

$Average \ \ Velocity=\frac{Total \ \ Displacement}{Total \ \ time \ \ taken}$ , $\vec{V}_{avg}=\frac{\vec{S}_{net}}{t}$

Instantaneous Velocity-

It is Velocity at that particular instant or small interval of time.
Formula-

$\vec{V}_{inst}= \lim_{\Delta t\rightarrow 0}\frac{\vec{\Delta x}}{\Delta t}$

V. Uniform motion and Non uniform motion

Uniform motion-

If equal distance/displacement is covered in equal intervals of time,how small these intervals may be.
Uniform speed-If equal distance are covered in equal intervals of time.
Uniform velocity-If equal displacement are covered in equal intervals of time.
Uniform speed and Uniform velocity is same as uniform motion.
For uniform motion along a straight line, the average and instantaneous velocities have the same values.

Non uniform motion-

If equal distance/displacement is covered in unequal intervals of time.
Non uniform speed-If equal distance are covered in unequal intervals of time.
Non uniform velocity-If equal displacement are covered in unequal intervals of time.
Non uniform speed and Non uniform velocity is same as Non uniform motion