Motion problems


Motion problems:- 

Today in this article I will discuss on the topics motion problems of unifom motion, hope this will help school going children especially for class( ix) and class (x) children. To start my discussion ,first we will know some important terms besides these motion is impossible,and these terms are,motion,initial velocity,final velocity, distance,time,acceleration,retardation etc.Let's try to know what these are:-

    *What is motion?

    Answer:- In science, the change of state of rest of rigid body and it travels a certain distance by the application of an external force is termed as motion of that perticular body.

    *What is initial velocity?


    Motion problems

    The starting velocity which a moving body gains when it is  in motion is called initial velocity. It is denoted by 'u'

    * What is acceleration?

    Answer:- The rate of change of increase in velocity of a moving body is called it's acceleration.It is denoted by 'a' and its S.I unit is m/s².

    *What is retardation?

    Answer:- The rate of decrease in velocity of a moving body is called retardation.It is also denoted by 'a' but it's value is always negative.

    *Motion problems:-

    Question(i):- Starting from rest a car travels a distance of .4km with an acceleration of 200cm/s²,find its final velocity.

    Motion problems

    Answer:- Initially car was at rest,

             so, It's initial velocity(u) = 0
             Distance(S)= .4km
                    = (.4×1000)m [∵1km=1000m]
                    = 400.0m
                    = 400m
         Acceleration(a) = 200cm/s²,
                      = 200/100m/s²[∵100cm=1m]
                      = 2m/s²
       Let,  final velocity = v
    ∵ we know that
         v²= u²+ 2aS [In case of uniform motion]
       =>v²= 0² + 2×2×400[ putting values]
       =>v²= 1600
       => v =√1600
       => v = 40
    ∴ Final velocity of the car = 40m/s²

    Question(ii):-  A moving body in a uniform motion  covers a distance 500m with an initial velocity 10m/s at a time interval of 20 sec, find its acceleration.

    Answer:- ∵ Distance(S) = 500m

                   Initial velocity(u)= 10m/s
                     Time(t) = 20sec
       Let, it's acceleration(a) = a
          ∵ we know that,
            S = ut + ½ at²
         =>500 = 10× 20 +½× a× 20²
          =>500 = 200 + ½× a × 400
          =>500-200 = a× 200
          =>300 =200×a
            =>a = 300/200
           => a = 1.5
    ∴ Acceleration(a) = 1.5m/s²

    Question(iii):- A bike was travelling with a speed of 72km/hr,10 sec later, it was stopped, find its retardation.

    Answer:- ∵ Here,

      Initial velocity of the bike(u) =72km/hr
                                  = 72×1000/60×60m/sec
                  [∵1km = 1000m and 1hr=3600sec]
                                  = 72000/3600m/sec
                                  =720/36 m/sec
                                  = 20 m/sec
               Time (t) = 10 sec
        Final velocity (v) =0
       Let ret retardation = a
    ∴ we know that,
                  v = u + at [∵ In case of retardation]
              =>0 = 20 + a×10
             => -20 = a×10
             => a = -2
    ∴ Retardation or negative acceleration (a)
                                     = - 2m/s²

      Problems on free falling bodies :-

      Question(a):-A stone is thrown upwards direction  with a velocity of 20m/sec and 5 sec later it falls back to the ground, find the highest distance it travelled.


            Here, Initial velocity of the stone(u)
                                        = 20 m.sec⁻¹
                  Final velocity (v) = 0
                Time (t) = 5 sec
         Acceleration due to gravity (g) = 10m/s² [Here, value of 'g' has been assumed]
      Let, the stone travelled highest distance 
                                        = h meter
    ∵ we know that,
            v² = u²- 2gh [ ∵ The stone is thrown upwards direction,which is opposite of center of the direction of earth,so acceleration due to gravity will be negative]
         =>0² = 20² - 2 × 10 × h
          =>0 = 400 - 20h
          => 20 h = 400 
          => h = 400/20
         => h = 20
    ∴ Highest distance the stone travelled(h)
                                  = 20 meter

    Question(b):- An object falls at a height of 40m above the ground and touches the ground after 10 sec, find its acceleration.

    Answer:- Here,

                height of the object (h) = 30m
                Initial velocity (u) = 0
                time(t) = 10 sec
     Let acceleration due to gravity = g m.s⁻²
         ∵ h = ut + ½ gt²
         =>30 = 0 ×10 + ½ × g × 10² [ ∵ The is falling in the direction in earth's center,so acceleration due to gravity will be positive]

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    An object's mass in earth is 60 kg,what will be it's mass in moon ?

    Answer:- ∵ We know that, mass of earth =6×mass of moon =>mass of the body in moon = 1/6 × mass of body at earth => mass of the body in moon = 1/6 × 60 [∵ the mass of the body = 60 kg ] ∴ mass of the body in moon = 10 kg

    What is uniform acceleration?

    Answer:- When rate of change of increase in velocity of a moving remains equal in equal interval of time through out it's complete journey,then the acceleration is called uniform acceleration.

    Why second comes two times in the unit of acceleration?

    Answer:- We know, rate of change of increase in velocity is acceleration.So acceleration = velocity/time = m/sec/time [writing unit ofvelocity] = m/sec/sec [ writing unit of time] = m/sec², So second comes two times in the unit of acceleration.

    What will be the momentum of a body which is at rest?

    Answer:- We know momentum of a moving body is the product of its mass and velocity,ie; momentum = mv ∵ velocity (v) of a body which is at rest = 0 ∴ momentum = m × 0 = 0 So,momentum of a body, which is at rest is zero.

    What are the two types of motion?

    Answer:- Two types of motion are :- (i) Rectilinear motion (ii) Oscillatory motion.

    What type of quantities are distance and displacement?

    Answer:- Distance is a scaler quantity,where as displacement is a vector quantity.

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