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a body moving with uniform retardation covers 3 km before its speed is reduced to half of its initial value. it comes to rest t in another distance of?

If you plot the velocity of this moving object as a function of time the resulting graph is diagonal straight line with a negative slope. The area under a velocity time graph is equal to the displacement.

Since the acceleration is uniform the time to bring the object to rest will be same as the time to bring the velocity to one half its original value.

That means that the area between t=0s and t=t will be 3000m while the area between t=t and t=2t will be equal to 1000m!

Please see the attached graph.

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.