A point moving in a straight line travels in its second, ` 16 m, 28 m in 2nd and 5th sec` respectively , prove that point is moving with constant acceleration. Aso find the total distance moving by particle in ` 10 seconds.

Options

A. (a) both Assertion and Reason are true and the Reason is correct explanation of the Assertion .
B. (b )both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.
C. (C ) Assertion is true but the Reason is false.
D. (d) both Assertion and Reason are false.

Explanation

Let the initial velocity be (u) and acceleration be (a). Distance travelled in trvelled in `nth` scond by a particle moving in a straight line with a constant acceleration is
` D_n =u = a/2 (2 n-1)`
So, ` 16 = u + a/2 (2 xx 5- 1)` ..(i)
` 28 =u + a/2 (2 xx 5 -1)` ...(ii)
and ` 52 = u + a/2 (2 xx 11 -1)` ...(iii)
On solving (i). (ii) and (iii), we get
` a=4 ms^(-2), u = 10 ms^(-1)`
Now, ` S= ut 1/2 at^2 = 10 x 10 + 1/2 xx 4 xx 10^2`
`= 300 m= 100 a s`
:. ` a=3`.