Question

An object is dropped from rest calculate it's velocity after 2.5 sec if it is dropped:
a) On earth where acceleration due to gravity is 9.8 m per sec sq
b) On Mars where acceleration due to gravity is 3.8 m per sec sq

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

★ First Case :

Initial Velocity (u) = 0 m/s

Acceleration (a) = 9.8 m/s²

Time taken (t) = 2.5 sec

We know that,

$\Large{\implies{\boxed{\boxed{\sf{a = \frac{v - u}{t}}}}}}$

____________[Put Values]

$\sf{→ 9.8 = \frac{v - 0}{2.5}} \\ \\ \sf{→ 9.8 = \frac{v}{2.5}} \\ \\ \sf{→ v = 9.8 \times 2.5} \\ \\ \sf{→ v = 24.5 \: ms^{-1}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{v = 24.5 \: ms^{-1}}}}}}$

$\rule{200}{2}$

★ Second Case :

Inital Velocity (u) = 0m/s

Acceleration (a) = 3.8 m/s²

Time taken (t) = 2.5 sec

Now,

$\Large{\implies{\boxed{\boxed{\sf{a = \frac{v - u}{t}}}}}}$

____________[Put Values]

$\sf{→ 3.8 = \frac{v - 0}{2.5}} \\ \\ \sf{→ 3.8 = \frac{v}{2.5}} \\ \\ \sf{→ v = 3.8 \times 2.5} \\ \\ \sf{→ v = 9.5 \: ms^{-1}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{v = 9.5 \: ms^{-1}}}}}}$

Answer 2

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

• For g = 9.8 m/s² = 24.5 m/s

• For g = 3.8 m/s² = 9.5 m/s

$\rule{200}{0.5}$

$\underline{\underline{\mathfrak{Step-By-Step-Explanation :}}}$

Given :

• Time (t) = 2.5 s
• Initial velocity (u) = 0 m/s

_______________________

To Find :

• Final velocity when g = 9.8 m/s²
• Final velocity when g = 3.8 m/s²

________________________

Solution

• When g = 9.8 ms²

Use 1st equation of motion :

$\large{\boxed{\sf{v \: = \: u \: + \: gt}}} \\ \\ \implies {\sf{v \: = \: 0 \: + \: 9.8 \: \times \: 2.5}} \\ \\ \implies {\sf{v \: = \: 24.5}} \\ \\ \underline{\sf{\therefore \: Final \: velocity \: when \: g \: is \: 9.8 \: ms^{-2} \: is \: 24.5 \: ms^{-1}}}$

_________________________

• When g = 3.8 m/s²

Again use 1st equation of motion :

$\large{\boxed{\sf{v \: = \: u \: + \: gt}}} \\ \\ \implies {\sf{v \: = \: 0 \: + \: 3.8 \: \times \: 2.5}} \\ \\ \implies {\sf{v \: = \: 9.5}} \\ \\ \underline{\sf{\therefore \: Value \: of \: Final \: velocity \: when \: g \: = \: 3.8 \: ms^{-2} \: is \: 9.5 \: ms^{-1}}}$