Question

a body wuth initial velocity of 18km/hr accelerates uniformly at the rate od 9cm/s² over a distance of 200m. calculate: 1. the acceleration in m/s², 2. the final velocity in m/s.
plz help​

Answer 1

Explanation:

Vo = 18km/h =18000m/3600s=5m/s=Initial

velocity

1b. V^2 = Vo^2 + 2ad

V^2 = 5^2 ++ 0.18*200 = 61

V = 7.81 m/s. = Final velocity.

Answer 2

Given information :

• Initial velocity = 18 km/hr = 18 × 1000/3600 = 5 m/s
• Acceleration = 9 cm/s²
• Distance travelled = 200 m

To calculate :

1. The acceleration in m/s²
2. The final velocity in m/s

Solution :-

$\underline{ \sf{ \purple{(1) \: The \: acceleration \: in \: m/s^2 :- }}}$

We know that,

• 1 cm/s² = 0.01 m/s²

So, by substituting values,

$\dashrightarrow \: \: \sf Acceleration = 9 \times 0.01 \: m/s^2$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \underline{\boxed{ \pink{ \pmb{Acceleration = 0.09 \: m/s^2}}}}$

$\underline{ \sf{ \therefore \: Acceleration \: in \: m/s^2 \: is \: \: \bf 0.09 \: m/s^2}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{ \sf{ \purple{(2) \: The \: final \: velocity \: in \: m/s :- }}}$

So, for calculating the final velocity in m/s, we will be using third equation of motion,

$\dag$Distance - velocity relation -

• $\large{\underline{ \boxed{ \rm{ \orange{v^2 = u^2 + 2as}}}}}$

Where,

• v denotes final velocity = need to find
• u denotes initial velocity = 5 m/s
• a denotes acceleration = 0.09 m/s²
• s denotes distance travelled = 200 m⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Inserting the values in the equation,

$\dashrightarrow \: \: \sf v^2 = 18^2 + 2 \times 0.09 \times 200$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \sf v^2 = (5 × 5) + 2 \times 0.09 \times 200$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \sf v^2 = 25 + 2 \times 0.09 \times 200$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \sf v^2 = 25 + 36$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \sf v^2 = 61$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \sf v = \sqrt{61}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \underline{ \boxed{ \pmb{ \pink{Final \: velocity_{(in \: m/s)} = 7.81 \: m/s}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{ \sf{ \therefore \: The \: final \: velocity \: is \: \: \bf 7.81 \: m/s}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Knowledge BoosteR :

There are three equations of motion :-

1. First equation of motion :

This motion signifies the velocity time relation :

• $\large{\underline{ \boxed{ \rm{ \gray{v = u + at}}}}}$

2. Second equation of motion :

This motion signifies the distance time relation :

• $\large{\underline{ \boxed{ \rm{ \gray{s = ut + \dfrac{1}{2} at^2}}}}}$

3. Third equation of motion :

This motion signifies the distance - velocity relation :

• $\large{\underline{ \boxed{ \rm{ \gray{v^2 = u^2 + 2as}}}}}$