Motion in a Straight Line

Motion in a Straight Line

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Mechanics

Physical World, Units and Measurements
Motion in a Straight Line
Motion in a Plane
Laws of Motion
Work, Energy and Power
Gravitation
Mechanical Properties of Solids
Mechanical Properties of Fluids
System of Particles and Rotational Motion
  1. A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is








  1. View Hint View Answer Discuss in Forum

    Let PQ = x , then

    a =
    40² - 30²
    		 =
    350
    2xx

    [ ∵  v² = u² + 2as]
    Also, velocity at mid point is given by
    v² - 30² = 2 ×
    350
    		 ×
    x
    x2

    This gives v = 25√2 km/h

    Correct Option: C

    Let PQ = x , then

    a =
    40² - 30²
    		 =
    350
    2xx

    [ ∵  v² = u² + 2as]
    Also, velocity at mid point is given by
    v² - 30² = 2 ×
    350
    		 ×
    x
    x2

    This gives v = 25√2 km/h

  1. A bus is moving with a speed of 10 ms–1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the
    bus?








  1. View Hint View Answer Discuss in Forum

    Let v be the relative velocity of scooter
    w.r.t bus as v = vs– vB
    v = 1000/100 = 10ms-1vB = 10ms-1
    ∴ vS = v + vB, 

    = 10 + 10 = 20 ms-1
    ∴ velocity of scooter = 20 ms-1

    Correct Option: D

    Let v be the relative velocity of scooter
    w.r.t bus as v = vs– vB
    v = 1000/100 = 10ms-1vB = 10ms-1
    ∴ vS = v + vB, 

    = 10 + 10 = 20 ms-1
    ∴ velocity of scooter = 20 ms-1

  1. A train of 150 metre long is going towards north direction at a speed of 10 m/s . A parrot flies at the speed of 5 m/s towards south direction parallel to the railway track. The time taken by the parrot to cross the train is








  1. View Hint View Answer Discuss in Forum

    Relative velocity of parrot w.r.t the train
    = 10 – (–5) = 15 ms-1.
    Time taken by parrot to cross the train
    = 150/15 = 10s

    Correct Option: D

    Relative velocity of parrot w.r.t the train
    = 10 – (–5) = 15 ms-1.
    Time taken by parrot to cross the train
    = 150/15 = 10s

  1. A stone falls freely  under gravity. It covers distances h1, h4 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is








  1. View Hint View Answer Discuss in Forum

    ∵ h = 1/2 gt²
    ∴ h1 = 1/2 g(5)² = 125
    h1 + h2 = g(10)² = 500
    ⇒ h2 = 375
    h1 + h2 + h3 = g(15)² = 1125
    ⇒ h3 = 625
    h2 = 3h1 , h3 = 5h1
    or h1 = h2/3 = h3/5

    Correct Option: A

    ∵ h = 1/2 gt²
    ∴ h1 = 1/2 g(5)² = 125
    h1 + h2 = g(10)² = 500
    ⇒ h2 = 375
    h1 + h2 + h3 = g(15)² = 1125
    ⇒ h3 = 625
    h2 = 3h1 , h3 = 5h1
    or h1 = h2/3 = h3/5

  1. A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18s. What is the value of v?​​[2010] (take g = 10 m/s²)








  1. View Hint View Answer Discuss in Forum

    Clearly distance moved by 1st ball in 18s = distance moved by 2nd ball in 12s.
    Now, distance moved in 18 s by 1st ball = 1/2 × 10 × 18² = 90 × 18 = 1620 m
    Distance moved in 12 s by 2nd ball
    = ut + gt²
    ∴ 1620 = 12 v + 5 × 144
    ⇒ v = 135 – 60 = 75 ms–1

    Correct Option: A

    Clearly distance moved by 1st ball in 18s = distance moved by 2nd ball in 12s.
    Now, distance moved in 18 s by 1st ball = 1/2 × 10 × 18² = 90 × 18 = 1620 m
    Distance moved in 12 s by 2nd ball
    = ut + gt²
    ∴ 1620 = 12 v + 5 × 144
    ⇒ v = 135 – 60 = 75 ms–1