Question

Obtain an expression for the acceleration in terms of two distance travelled by a body along a
straight line in two successive equal intervals of time,​​

Answer 1

Answer:

Consider a particle moving with uniform acceleration a. Let it start from a point with initial velocity ‘u’ and covers the distances s

1

and s

2

in two successive equal intervals of time ‘t’ each. Distance covered in the first interval

s

1

=ut+1/2at

2

………. (1)

Distance covered at the end of time 2t,

s

1

+s

2

=u(2t)+1/2a(2t)

2

s

1

+s

2

=2ut+2at

2

……………. (2)

(s

1

+s

2

)–2s

1

=(2ut+2at

2

)–(2ut+at

2

)

s

2

–s

1

=at

2

a=

t

2

s

2

−s

1

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