Question

A body moving in a straight line covers a distance of 14m in the 5th second and 20 m in the 8th second. How much distance will it cover in the 15th second ?

Answer 1

Answer - 34 m

Explanation -

Consider distance formula, s = ut + at2/2. This gives the total distance travelled in t seconds. But, the given data is of tth second and not total t seconds.

So, consider for 5th second first. S5 = distance travelled

in 5 seconds - distance travelled in 4 seconds. S5 = [(5u +

25a/2) - (4u +16a/2)]. You will get S5=14 = u +9a/2.

Similarly, find Sg 20 u+15a/2.

So, now you have 2 equations. Solve them to get the values of 'u' and 'a'. Once you subtract them, you will get 'a' = 2 m/s2.

Then you multiply one equation by 10 and the other by 6. Then subtract the two equations and solve to get 'u'. You will get u = 5 m/s.

Finally use the values of u and a to get S15 = [(15u + 225a/2) - (14u+ 196a/2)] = u + 29a/2 = 34 m.