Question

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

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

Solution

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 + Bt^2,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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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

What is a scalar quantity?

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

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