Question

a body moving with velocity 40 metre per second is brought to rest in 20 seconds find out the retardation find also the distance travelled in that time ​

Answer 1

Given :

• Initial velocity, u = 40 m/s

• Final velocity, v = 0 m/s (as it brought to rest)

• Time, t = 20 seconds

To find :

• Retardation, a
• Distance travelled, s

According to the question,

➞ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

➞ 0 = 40 + a × 20

➞ 0 - 40 = 20a

➞ - 40 = 20a

➞ - 40 ÷ 20 = a

➞ - 2 = a

So,the retardation is - 2 m/s².

Now,

➞ v² = u² + 2as

Where,

• a = Acceleration
• s = Distance
• u = Initial velocity
• v = Final velocity

➞ (0)² = (40)² + 2 × (-2) × s

➞ 0 = 1600 + (-4s)

➞ 0 - 1600 = - 4s

➞ - 1600 = - 4s

➞ 1600 ÷ 4 = s

➞ 400 = s

So,the distance travelled is 400 meter.

Answer 2

Answer:

Given :-

• A body moving with velocity 40 m/s is brought to rest in 20 seconds.

To Find :-

• What is the retardation and the distance travelled by a body.

Formula Used :-

❶To find acceleration we know that,

$\boxed{\bold{\large{v\: =\: u\: +\: at}}}$

❷ To find distance travelled we know that,

$\boxed{\bold{\large{{v}^{2} =\: {u}^{2} +\: 2as}}}$

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time
• s = Distance travelled

Solution :-

❶ To find retardation,

Given :

• Final velocity = 0 m/s
• Initial velocity = 40 m/s
• Time = 20 seconds

According to the question by using the formula we get,

⇒ 0 = 40 + a(20)

⇒ 0 - 40 = 20a

⇒ - 40 = 20a

⇒ $\dfrac{\cancel{- 40}}{\cancel{20}}$ = a

⇒ - 2 = a

➠ a = - 2 m/s²

$\therefore$ The retardation of a body is - 2 m/s² .

❷ To find distance travelled,

Given :

• Final velocity = 0 m/s
• Initial velocity = 40 m/s
• Time = 20 seconds
• Acceleration = - 2 m/s²

According to the question by using the formula we get,

↦ (0)² = (40)² + 2(- 2) × s

↦ 0 = 1600 - 4 × s

↦ 0 = 1600 - 4s

↦ 0 - 1600 = - 4s

↦ - 1600 = - 4s

↦ $\dfrac{\cancel{- 1600}}{\cancel{- 4}}$ = s

↦ 400 = s

➥ s = 400 m

$\therefore$ The distance travelled by a body is 400 m .