Question

A body has initial velocity of 3 m/s and has an
acceleration of 2 m/s². The distance travelled
by it in 5 s and its velocity is
(A) 40 m, 13 m/s (B) 10 m, 13 m/s
(C) 40 m, 10 m/s (D) 10 m, 10 m/s​

Answer 1

Given :

• Initial velocity, u = 3 m/s
• Acceleration, a = 2 m/s²
• Time taken, t = 5 seconds

To find :

• Final velocity, v
• Distance travelled, s

According to the question,

➟ v = u + at

Where,

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

➟ v = 3 + 2 × 5

➟ v = 3 + 10

➟ v = 13

• So, the final velocity is 13 m/s.

Now,

➟ s = ut + ½ at²

Where,

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

➟ s = 3 × 5 + ½ × 2 × 5 × 5

➟ s = 15 + 25

➟ s = 40

• So, the distance travelled by the body is 40 m.

Hence, option (A) 40 m, 13 m/s is correct.

Answer 2

$\Large\orange\star\:{\underline{\boxed{\tt{\pink{(A)\:40\:m\:,\:13\:m/s}}}}}\:\green\star$

$\Large{\purple{\underline{\textsf{\textbf{Step-by-step\:Explanation\::}}}}}$

Gɪᴠᴇɴ :

• Initial velocity of a body is 3 m/s.

$:\longrightarrow\:\:\bf{Initial\:velocity\:(u)\:=\:3\:m/s}$

• Acceleration of the body is 2 m/s².

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

• Time period is 5 seconds.

$:\longrightarrow\:\:\bf{Time\:(t)\:=\:5\:s}$

Tᴏ Fɪɴᴅ :

1. Distance travelled by the body.
2. Velocity of the body.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

☆ For calculating the distance travelled by the body, we use the following formula.

↝ Using equation of motion as,

$\pink\bigstar\:\:{\underline{\green{\boxed{\bf{\purple{S\:=\:u\:t\:+\:\dfrac{1}{2}\:a\:t^2\:}}}}}}$

Wʜᴇʀᴇ,

• S is the distance travelled by the body.

• u is the initial velocity, i.e. 3 m/s.

• t is the time period, i.e. 5 seconds.

• a is acceleration of the body, i.e. 2 m/s².

➛ $\sf{S\:=\:3\times{5}\:+\:\dfrac{1}{2}\times{2}\times{5^2}\:}$

➛ $\sf{S\:=\:15\:+\:25\:}$

➛ $\bf\blue{S\:=\:40\:m}$

$\Large\bf{Therefore,}$

❶ The distance travelled by the body is 40 m.

Nᴏᴡ,

☆ For calculating the velocity travelled by the body, we use the following formula.

↝ Using equation of motion as,

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{v\:=\:u\:+\:a\:t\:}}}}}}$

➙ $\sf{v\:=\:3\:+\:2\times{5}\:}$

➙ $\sf{v\:=\:3\:+\:10\:}$

➙ $\bf\pink{v\:=\:13\:m/s}$

$\Large\bf{Therefore,}$

❷ The velocity of the body is 13 m/s.