Q21 of 24 Page 31

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.

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 d1, let the time taken to travel be t1 then





And also for d2, let the time taken to travel be t2 then





Now total time to travel will be t1 + t2



More from this chapter

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19

Can the direction of velocity of an object reverse when it’s acceleration is constant? If so give an example; if not, explain why.

 20

A 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.

 22

You 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.

 23

A train of length 50m is moving with a constant speed of 10m/s. Calculate the time taken by the train to cross an electric pole and a bridge of length 250 m.