Question

A partical moving with uniform acceleration covers 10 m in 5th sec and 15metre in 10th sec.find the distance travelled by the particle in 15th sec​

Answer 1

Answer:

$S_{15}$=20m

Explanation:

Given,

The distance travelled in 5th second=10m

The distance travelled in 10th second=15m

NOTE: The distance travelled by the body in nth second=>$S_{n}$=u+$\frac{a}{2}${2n-1}

Using above formula,

$S_{5}$=10                                                      |   $S_{10}$=15

10=u+$\frac{a}{2}${2(5)-1}                                        |   15=u+$\frac{a}{2}${2(10)-1}

10=u+$\frac{9a}{2}$------(1)                                        |  15=u+$\frac{19a}{2}$------(2)

So, when we will simplify the above two equations,

(2)-(1)=>5=5a                                    |  Substitute eq.(3) in (1):

       =>a=1 m$s^{-2}$-------(3)                  |     u=$\frac{11}{2}$m$s^{-1}$-------(4)

Then,

$S_{15}$=$\frac{11}{2}$+$\frac{1}{2}${30-1}

$S_{15}$=20m