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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?


Speed of the cyclist, v = 27 km/h = 7.5 m/s

Radius of the circular turn, r = 80 m

Centripetal acceleration is,

     straight a subscript straight c space equals space straight v subscript straight c squared over straight r equals fraction numerator left parenthesis 7.5 right parenthesis to the power of 2 space end exponent over denominator space 80 space end fraction equals space 0.7 space ms to the power of negative 2 end exponent
The question can be illustrated in the figure as shown below:



Consider, the cyclist begins cycling from point P and moves toward point Q. 

At point Q, he applies the breaks and decelerates the speed of the bicycle by 0.5 m/s2

This acceleration is along the tangent at Q and opposite to the direction of motion of the cyclist.

The angle between ac and aT is 900. Therefore, the resultant acceleration a is given by,

straight a space equals space left parenthesis straight a subscript straight c to the power of 2 space end exponent plus space straight a subscript straight T squared right parenthesis to the power of 1 divided by 2 end exponent space

space space space equals space open square brackets left parenthesis 0.7 right parenthesis squared space plus space left parenthesis 0.5 right parenthesis squared space close square brackets to the power of 1 divided by 2 end exponent space

space space space space equals space left parenthesis 0.74 to the power of right parenthesis 1 divided by 2 end exponent space

space space space space equals 0.86 space ms to the power of negative 2 end exponent space

tan space straight theta space equals space fraction numerator straight a subscript straight c over denominator space straight a subscript straight T end fraction comma space space straight theta space is space the space angle space of space the space resultant space
with space the space direction space of space velocity.

space space space space space space space tan space straight theta space equals space fraction numerator 0.7 over denominator 0.5 end fraction space equals space 1.4 space
rightwards double arrow space straight theta space space equals space space space tan to the power of negative 1 end exponent space left parenthesis 1.4 right parenthesis space equals space 54.56 to the power of straight o

Therefore comma space the space magnitude space of space the space net space
acceleration space of space the space cyclist space is space 0.86 space ms to the power of negative 2 end exponent space
making space an space angle space of space 54.56 to the power of straight o space with space the space direction space of space velocity. space
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Give three examples of vector quantities.

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

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What is a scalar quantity?

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What is a vector quantity?

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