Question

a body starts from rest and is accelerated uniformly. find the ratio of the distance travelled by the body in 1st ,3rd and 5th seconds

Answer 1

To find:

The ratio of the distance travelled by the body in 1st, 3rd and 5th seconds.

Solution:

» S = ut+ ½ at²

And S (n -1) = u (t - 1) + ½ a (t - 1)²

Now, S - S (n - 1) = Sn

» Sn = ut - ut + u + ½ at² - ½ at² + 2at - a

» Sn = u + 2at - a

» Sn = u + a (2t - 1) ... distance travelled in nth second.

Therefore,

» S1 = a [2 (1) - 1] = a

» S3 = a [2 (3) - 1] = 5a

» S5 = a [2 (5) - 1] = 9a

Hence, S1 : S3 : S5 = 1 : 5 : 9