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Motion In Straight Line

Question
CBSEENPH11026198
Wired Faculty App

A particle moves along a straight line OX. At a time t (in second) the distance x ( in metre ) of the particle from O is given by x = 40 + 12 t - t3 . How long would the particle travel before coming to rest?

  • 24 m

  • 40 m

  • 56 m

  • 16 m

Solution

C.

56 m

Speed is rate of change of distance.

Distance travelled by the particle is

               x = 40 + 12 t - t3

We know the speed is rate of change of distance

       i.e       ν = dxdt

                  ν = ddt40 + 12t - t3

                     = 0 + 12 - 3t2

but final velocity ν = 0

∴               12 - 3t2 = 0

⇒               t2 = 123   t2 = 4

 ⇒              t = 2s

Hence, distance travelled by the particle before coming to rest is given by
             x = 40 + 12(2)-(2)3

             x = 64 - 8

              x = 56 m

Some More Questions From Motion in Straight Line Chapter

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.

Define displacement.

Can magnitude of displacement be greater than distance travelled by particle?

A body is thrown with a velocity of 9.8 m/s in the vertical upward direction. What is the velocity after one second?

How does the displacement of a particle change, when reference point for the position is shifted?

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