Question

The initial velocity of a body moving along a straight line is 8 u. It has a uniform acceleration of 6 ms. The distance covered by the body in the 6 second of its motion is 41 m. The value of u is b) 12 ms- 8 ms- d) 4 ms- 1 ​

Answer 1

Given :-

Initial velocity of the body is 8u

Acceleration of the body is a= 8 m/s²

Distance covered is sn= 41m

Time is 6th second (n= 6)

¤ Required to find :-

Value of u

Formula to be noted :-

$\: \: \clubs \boxed{ \bf \red{s_n = u + a \bigg(n - \frac{1}{2} \bigg) }}$

Solution:-

Substituting the values ,

$\implies \bf \: 41 = 8u + \: 6 \bigg(6 - \dfrac{1}{2} \bigg)$

$\implies \bf \: 41 = 8u + \: 6 \bigg( \dfrac{12 - 1}{2} \bigg)$

$\implies \bf \: 41 = 8u + \: \not6 \tiny{3} \: \bigg( \large \dfrac{11}{ \not2} \bigg)$

$\implies \bf \: 41 = 8u + \: 3(11)$

$\implies \bf \: 41 = 8u + \: 33$

$\implies \bf \: 41 - 33 = 8u$

$\implies \bf \: 8 = 8u$

$\implies \bf \: u \: = \dfrac{8}{8}$

$\implies \bf \: u \: = 1 \: ms {}^{ - 1}$

$\sf \pink{ \underline{Initial \: velocity \: of \: the \: body \: is \: 1ms {}^{ - 1}}}$

Know more :-

♣ Equations of motion:-

v = u + at

s = ut + ½ at²

v² - u² = 2as

where,

v = final velocity

u = initial velocity

a = acceleration

t = time taken

s = distance covered