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Speed And Velocity - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Speed and velocity is considered one of the most asked concept.

  • 36 Questions around this concept.

Solve by difficulty

A body moving along a straight line travels one-third of the total distance with a speed of 3m{{s}^{-1}}. The remaining distance is covered with a speed of 4m{{s}^{-1}} for the half time and 5m{{s}^{-1}} for the other half-time. The average speed during the motion is :

The distance travelled by a particle is related to time t as x= 4t^{2} . The velocity of the particle is :

The distance travelled by an object in time t is given bys = (2.5)t^2. The instantaneous speed of the object at t =5 s will be :

The position of a particle related to time is given by x=(5t^{2}-4t+5)m .  The magnitude of the velocity of the particle at t = 2s will be :

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 }{time}

 

  • Tips of Speed-

  1. S.I. unit\rightarrow ms^{-1} or meters per second.

  2. Dimensions=LT^{-1}

  3. Speed is a scalar quantity.

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

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

 

II .   Average Speed and Instantaneous Speed

  

  1.  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}}

 

  1.  Instantaneous Speed-

  • It is the 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-

  1. S.I. unit \rightarrow  m/s

  2. Dimensions-LT^{-1}

  3. Velocity is a vector quantity. 

  4. Velocity is also called speed in a definite (particular) direction.

 

IV.    Average Velocity  and Instantaneous Velocity

  1. Average Velocity-

  • Amount of total displacement covered in total time.

  • Formula-

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

 

  1.   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

 

  1. Uniform motion-

  • If equal distance/displacement is covered in equal intervals of time, how small these intervals may be.

  • Uniform speed-If equal distances 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 the same as uniform motion.

  • For uniform motion along a straight line, the average and instantaneous velocities have the same values.

  1. Non-uniform motion

  •  If equal distance/displacement is covered in unequal intervals of time.

  • Non-uniform speed-If equal distances 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

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Speed and velocity

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