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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

Starting from rest, a train travels with a constant acceleration of...

Starting from rest, a train travels with a constant acceleration of 2.0 m/s22.0 \text{ m/s}^2 for half a minute. Subsequently, the brakes are applied, bringing the train to rest in one minute. Determine the total distance moved by the train in km.

Options

  1. A0.90.9
  2. B1.81.8
  3. C27002700
  4. D2.72.7

Correct answer

D. 2.72.7

Step-by-step solution

For the acceleration phase:
Initial velocity, u=0u = 0
Acceleration, a1=2.0 m/s2a_1 = 2.0 \text{ m/s}^2
Time, t1=0.5 min=30 st_1 = 0.5 \text{ min} = 30 \text{ s}

Maximum velocity reached, v=u+a1t1=0+2.0×30=60 m/sv = u + a_1 t_1 = 0 + 2.0 \times 30 = 60 \text{ m/s}

Distance covered during acceleration, s1=12a1t12=12×2.0×(30)2=900 ms_1 = \dfrac{1}{2} a_1 t_1^2 = \dfrac{1}{2} \times 2.0 \times (30)^2 = 900 \text{ m}

For the deceleration phase:
Initial velocity, v=60 m/sv = 60 \text{ m/s}
Final velocity, vf=0v_f = 0
Time, t2=1 min=60 st_2 = 1 \text{ min} = 60 \text{ s}

Distance covered during deceleration, s2=v+vf2t2=60+02×60=1800 ms_2 = \dfrac{v + v_f}{2} t_2 = \dfrac{60 + 0}{2} \times 60 = 1800 \text{ m}

Total distance moved by the train, s=s1+s2=900+1800=2700 ms = s_1 + s_2 = 900 + 1800 = 2700 \text{ m}

Converting to kilometers, s=2.7 kms = 2.7 \text{ km}
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