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Q. 214.4( 7 Votes )

Consider a train which can accelerate with an acceleration of 20cm/s² and slow down with deceleration of 100cm/s². Find the minimum time for the train to travel between the stations 2.7 km apart.

Class 9th AP - Physics & Chemistry 2. Motion

Answer :

Given, total distance need to cover, d = 2.7km = 270000 cm

Let distance covered in accelerated motion be d₁ and distance covered in decelerated motion be d₂.

So, d₁ + d₂ = d …(1)

Now for d₁, initial velocity will be 0, and acceleration a = 20 cm/s² and let final velocity be v.

Then,

Now for d₁, initial velocity will be v, and acceleration a’ = 100 cm/s² and velocity will be 0.

Then,

Now putting values of d, d₁ and d₂ in equation (1), we get

And also for d_1, let the time taken to travel be t₁ then

And also for d_2, let the time taken to travel be t₂ then

Now total time to travel will be t₁ + t₂

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PREVIOUSA point mass starts moving in a straight line with constant acceleration “a”. At a time t after the beginning of motion, the acceleration changes sign, without change in magnitude. Determine the time t0 from the beginning of the motion in which the point mass returns to the initial position.NEXTYou may have heard the story of the race between the rabbit and tortoise. They started from same point simultaneously with constant speeds. During the journey, rabbit took rest somewhere along the way for a while. But the tortoise moved steadily with lesser speed and reached the finishing point before rabbit. Rabbit awoke and ran, but rabbit realized that the tortoise had won the race. Draw distance vs time graph for this story.

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