Q20 of 24 Page 31

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.

Given, acceleration = a, initial velocity = 0 and time = t


Velocity after time t, v = …(1)


Now it will become initial velocity.


After acceleration change its sign, let time taken by it to come to rest be t’,



…(2)



Total time = t + t’


Now distance covered in total time


=


=


=


=


=


=…(3)


Now after coming to rest it will again start moving in opposite direction. To reach initial point, it has to cover same distance,


So let time taken to cover that distance be t”. Here initial velocity will be 0. Putting value of distance from equation (3), we get.




Time t0



=


More from this chapter

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18

When the velocity is constant, can the average velocity over any time interval differ from instantaneous velocity at any instant? If so, give an example; if not explain why.

 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.

 21

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.

 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.