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

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W} \purple{E}\orange{R᭄}}}}$

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

${\tt{\red{\underline{\underline{\huge{Solution:}}}}}}$

$\begin{gathered}\green\bigstar\:\:{\underline{\green{\boxed{\bf{\pink{(A)40m,13m/s}}}}}} \\ \end{gathered} \: \: \orange\bigstar$

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

Gɪᴠᴇɴ :

• Initial velocity of a body is $\bold{3\: m/s.}$

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

• Acceleration of the body is $\bold{2\: m/s².}$

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

• Time period is $\bold{5 \:seconds.}$

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

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,

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

Wʜᴇʀᴇ,

• $\bold{S}$ is the distance travelled by the body.

• $\bold{u}$ is the initial velocity, i.e. $\bold{3\: m/s.}$

• $\bold{t}$ is the time period, i.e. $\bold{5 \:seconds.}$

• $\bold{a}$ is acceleration of the body, i.e. $\bold{2\: m/s².}$

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

$➛ \begin{gathered}\sf{S\:=\:15\:+\:25\:} \\ \end{gathered}$

$➛ \begin{gathered}\bf\blue{S\:=\:40\:m} \\ \end{gathered}$

$\Large\bf{Therefore,}$

❶ The distance travelled by the body is $\bold{40 \:m.}$

Nᴏᴡ,

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

↝ Using equation of motion as,

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

$➙ \begin{gathered}\sf{v\:=\:3\:+\:2\times{5}\:} \\ \end{gathered}$

$➙ \begin{gathered}\sf{v\:=\:3\:+\:10\:} \\ \end{gathered}$

$➙ \begin{gathered}\bf\pink{v\:=\:13\:m/s} \\ \end{gathered}$

$\Large\bf{Therefore,}$

❷ The velocity of the body is $\bold{13\: m/s.}$

Tʜᴀɴᴋs!!