Question

A body starts moving with an initial velocity of u m s–1 and an acceleration

of 4 m s–2. If the distance travelled by it is 20 m in the 2 second, then the

value of u is ________
​

Answer 1

Answer:

Explanation:

Given,

• Acceleration of the body, a = 4 m/s²
• Distance travelled by the body, s = 20 m/s
• Time taken by the body, t = 2 seconds

To Find,

• Initial velocity, u = ?

Formula to be used,

• 2nd equation of motion,
• s = ut + 1/2 × at²

Solution,

Putting all the values, we get

s = ut + 1/2 × at²

⇒ 20 = u × 2 + 1/2 × 4 × (2)²

⇒ 20 = 2u + 2 × 4

⇒ 20 = 2u + 8

⇒ 20 - 8 = 2u

⇒ 12 = 2u

⇒ 12/2 = u

⇒ u = 6 m/s

Hence, the initial velocity is 6 m/s.

Answer 2

Answer:

Given :-

• A body starts moving with an initial velocity of u m/s and an acceleration of 4 m/s².
• The distance travelled by it is 20 m in the 2 seconds.

To Find :-

• What is the initial velocity i.e, u.

Formula Used :-

$\clubsuit$ Second Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{s =\: ut + \dfrac{1}{2}at^2}}}$

where,

• s = Distance Covered
• u = Initial Velocity
• t = Time Taken
• a = Acceleration

Solution :-

Given :

$\bigstar\: \: \bf{Acceleration\: (a) =\: 4\: m/s^2}$

$\bigstar\: \: \bf{Distance\: Covered\: (s) =\: 20\: m}$

$\bigstar\: \: \bf{Time\: Taken\: (t) =\: 2\: seconds}$

According to the question by using the formula we get,

$\longrightarrow \sf 20 =\: u(2) + \dfrac{1}{2} \times (4)(2)^2$

$\longrightarrow \sf 20 =\: 2u + \dfrac{1}{2} \times 4 \times 2 \times 2$

$\longrightarrow \sf 20 =\: 2u + \dfrac{1}{2} \times 8 \times 2$

$\longrightarrow \sf 20 =\: 2u + \dfrac{1}{\cancel{2}} \times {\cancel{16}}$

$\longrightarrow \sf 20 =\: 2u + \dfrac{1}{1} \times 8$

$\longrightarrow \sf 20 =\: 2u + \dfrac{8}{1}$

$\longrightarrow \sf 20 =\: 2u + 8$

$\longrightarrow \sf - 2u =\: 8 - 20$

$\longrightarrow \sf {\cancel{-}} 2u =\: {\cancel{-}} 12$

$\longrightarrow \sf 2u =\: 12$

$\longrightarrow \sf u =\: \dfrac{\cancel{12}}{\cancel{2}}$

$\longrightarrow \sf u =\: \dfrac{6}{1}$

$\longrightarrow \sf\bold{\red{u =\: 6\: m/s}}$

${\small{\bold{\purple{\underline{\therefore\: The\: value\: of\: u(initial\: velocity)\: is\: 6\: m/s\: .}}}}}$