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Motion In Straight Line

Question
CBSEENPH11020793
Wired Faculty App

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by
        straight x equals 40 straight t space plus 12 straight t minus straight t cubed
How long would the particle travel before coming to rest?

  • 24m

  • 40m

  • 56m

  • 16m

Solution

C.

56m

Velocity is rate of change of distance or displacement.
Distance travelled by the particle is
                      straight x equals space 40 space plus 12 straight t minus straight t cubed
We know that, velocity is rate of change of distance i.e., straight v equals dx over dt.
therefore space space space straight v space equals space straight d over dt left parenthesis 40 plus 12 straight t minus straight t cubed right parenthesis space space space space space space equals space 0 plus 12 minus 3 straight t squared
but final velocity v = 0
therefore space space 12 minus 3 straight t squared space equals space 0 or space space space space space space space space straight t squared space equals space 12 over 3 space equals 4 or space space space space space space straight t space equals space 2 straight s
Hence, distance travelled by the particle before coming to rest is given by
                   straight x equals 40 plus 12 left parenthesis 2 right parenthesis minus left parenthesis 2 right parenthesis cubed space space equals 40 plus 24 minus 8 space equals space 64 minus 8 space space equals space 56 space straight m
            

Some More Questions From Motion in Straight Line Chapter

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

 A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: 

(a) A kite flying in the sky.

(b) The earth revolving around the sun. 

(c) A train moving along the equator of the earth in clockwise direction. 

(d) Accelerated motion of a particle in a straight line.

Define distance.

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