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Atoms And Molecules

Question
CBSEENSC9006122

Take data in Fig. 10.12 and find the value of ‘a’.




Solution

From A to B, 
u = 0 m/s, s = - 4.9 m, t = 1 sec
Now, using the 2nd equation of motion, 
space space space space straight s space equals space ut space plus space 1 half at squared space
space minus space 4.9 space equals space 0 plus 1 half straight a cross times left parenthesis 1 right parenthesis squared space
rightwards double arrow space space space space straight a space equals space minus 9.8 space straight m divided by straight s squared space

From space straight B space to space straight C comma space

Let space straight v subscript straight B space be space the space velocity space of space the space body space at space straight B. space
Now comma space

straight v space equals space straight u space plus straight a space straight t

therefore space straight v subscript straight B space equals space 0 space minus space 9.8 space cross times 1 space
space space space space space space space space space space equals space space minus 9.8 space straight m divided by straight s

Again comma space using space the space equation comma
space space space space straight s space equals space ut space plus space 1 half at squared space
minus 14.7 space equals space left parenthesis negative 9.8 cross times 1 right parenthesis space plus space 1 half cross times straight a cross times left parenthesis 1 right parenthesis squared space
So comma space minus 4.9 space equals space straight a over 2
rightwards double arrow space space straight a space equals space 9.8 space straight m divided by straight s squared

From space straight C space to space straight D comma space

Let space straight v subscript straight c space be space the space velocity space of space the space body space at space straight C. space

Using space the space first space equation space of space motion comma space we space have

straight v space equals space straight u space plus space at

straight v subscript straight c space equals space minus 9.78 space minus 9.8 cross times 1 space equals space minus 19.6 space straight m divided by straight s

Using space the space formula comma space
space space space straight s space equals space ut space plus space 1 half at squared space
minus 24.5 space equals space left parenthesis negative 19.6 cross times 1 right parenthesis space plus space 1 half cross times straight a cross times left parenthesis 1 right parenthesis squared space
minus 4.9 space equals space straight a over 2 space
rightwards double arrow space straight a space equals space minus 9.8 space straight m divided by straight s squared

Thus comma space the space acceleration comma space throughout space is space 9.8 space straight m divided by straight s squared
in space the space downward space direction. space