If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is, from Physics Motion in A Plane Class 11 Manipur Board
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If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is,

  • 3A + 7B

  • fraction numerator 3 over denominator 2 space end fraction A space plus space 7 over 3 B
  • straight A over 2 plus B over 3
  • fraction numerator 3 over denominator 2 space end fraction A space plus space 4 B

B.

fraction numerator 3 over denominator 2 space end fraction A space plus space 7 over 3 B

Velocity of the particles is given as,
v = At + Bt2, where a and B are constants.

rightwards double arrow space dx over dt space equals space At space plus space Bt squared space space open square brackets because space straight v space equals dx over dt close square brackets
rightwards double arrow space dx space equals space left parenthesis At space plus space Bt squared right parenthesis space dt
Integrating both sides, we get
space space space space space space integral subscript straight x subscript 1 end subscript superscript straight x subscript 2 end superscript space d x space equals space integral subscript 1 superscript 2 space left parenthesis A t space plus space B t squared right parenthesis space d t
increment x space equals space x subscript 2 space minus space x subscript 1
space space space space space space equals space A integral subscript 1 superscript 2 t. space d t space plus space B integral subscript 1 superscript 2 t squared. d t
space space space space space space equals space A open square brackets t squared over 2 close square brackets subscript 1 superscript 2 space plus space B space open square brackets t cubed over 3 close square brackets subscript 1 superscript 2
space space space space space space equals space A over 2 left parenthesis 2 squared space minus space 1 squared right parenthesis space plus space B over 3 left parenthesis 2 cubed minus space 1 cubed right parenthesis

Therefore, distance travelled between 1 s and 2 s is,

increment straight x equals straight A over 2 straight x left parenthesis 3 right parenthesis plus straight B over 3 left parenthesis 7 right parenthesis
space space space space space space equals space fraction numerator 3 straight A over denominator 2 end fraction plus fraction numerator 7 straight B over denominator 3 end fraction

Velocity of the particles is given as,
v = At + Bt2, where a and B are constants.

rightwards double arrow space dx over dt space equals space At space plus space Bt squared space space open square brackets because space straight v space equals dx over dt close square brackets
rightwards double arrow space dx space equals space left parenthesis At space plus space Bt squared right parenthesis space dt
Integrating both sides, we get
space space space space space space integral subscript straight x subscript 1 end subscript superscript straight x subscript 2 end superscript space d x space equals space integral subscript 1 superscript 2 space left parenthesis A t space plus space B t squared right parenthesis space d t
increment x space equals space x subscript 2 space minus space x subscript 1
space space space space space space equals space A integral subscript 1 superscript 2 t. space d t space plus space B integral subscript 1 superscript 2 t squared. d t
space space space space space space equals space A open square brackets t squared over 2 close square brackets subscript 1 superscript 2 space plus space B space open square brackets t cubed over 3 close square brackets subscript 1 superscript 2
space space space space space space equals space A over 2 left parenthesis 2 squared space minus space 1 squared right parenthesis space plus space B over 3 left parenthesis 2 cubed minus space 1 cubed right parenthesis

Therefore, distance travelled between 1 s and 2 s is,

increment straight x equals straight A over 2 straight x left parenthesis 3 right parenthesis plus straight B over 3 left parenthesis 7 right parenthesis
space space space space space space equals space fraction numerator 3 straight A over denominator 2 end fraction plus fraction numerator 7 straight B over denominator 3 end fraction

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