Question

a partical start its motion in a straight line with a constant acceleration if sn indicate the distance describe by the partical at nth second .The find the ratio S7:S13 .

Answer 1

Distance covered in n seconds is Sⁿ

Now, since the object starts from rest and thus initial velocity = 0 ms⁻¹

Now, Sⁿ = u*n + 1/2 *a*n²

But,

Sⁿ = (0)n + 1/2*a*n²

∴ Sⁿ = 1/2*a*n²

Now,

S₇ = 1/2 * a * (7)² = 1/2*a*49

and similarly,

S₁₃ = 1/2*a*(13)²= 1/2*a*169

And thus,

S₇ : S₁₃ = 49 : 169

Hope this helps you !!