Zigya Logo

Chapter Chosen

Motion in Straight Line

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

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


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

            

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

            

782 Views

What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest. 
1215 Views

Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself. 
746 Views

Is absolute rest or absolute motion possible?

Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion. 
1986 Views

What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion. 
657 Views

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

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion. 
650 Views