[tex]\bold{\huge{\underline{ Answer }}}[/tex]
Answer 1 :-
Here, We have
- Initial velocity = 0 , as jeepney started from rest
- Time = 2 seconds
- Distance = 20 m
Therefore,
By using second equation of motion
[tex]\sf{ S = ut {\times} }{\sf{\dfrac{1}{2}}}{\sf{at^{2}}}[/tex]
Subsitute the required values,
[tex]\sf{ 20 = 0{\times}2 {\times} }{\sf{\dfrac{1}{2}}}{\sf{{\times}a(2)^{2}}}[/tex]
[tex]\sf{ 20 = }{\sf{\dfrac{1}{2}}}{\sf{{\times}4a}}[/tex]
[tex]\sf{ 20 = 2a }[/tex]
[tex]\sf{ a = }{\dfrac{ 20}{2}}[/tex]
[tex]\sf{ a = 10\:m/s^{2}}[/tex]
Hence, The acceleration of the jeepeny is 10 m/s² .
Answer 2 :-
Here, we have
- Initial velocity = 0 , as the coins started rolling from rest.
- Acceleration = 4 m/s²
- Time = 3 seconds
Therefore,
By using second equation of motion
[tex]\sf{ S = ut {\times} }{\sf{\dfrac{1}{2}}}{\sf{at^{2}}}[/tex]
Subsitute the required values,
[tex]\sf{ S = 0{\times}3 {\times} }{\sf{\dfrac{1}{2}}}{\sf{{\times}4(3)^{2}}}[/tex]
[tex]\sf{ S = }{\sf{\dfrac{1}{2}}}{\sf{{\times}4(9)}}[/tex]
[tex]\sf{ S = }{\sf{\dfrac{1}{2}}}{\sf{{\times}36}}[/tex]
[tex]\sf{ S = 18 \: m }[/tex]
Hence, The coin will reach 18 m after 3 seconds.
Answer 3 :-
Here,
- A stone fell from a 45 m high cliff and hit the ground.
So,
- Initial velocity = 0
- Distance = 45 m
- Acceleration due to gravity
By using third equation of motion
[tex]\sf{ v^{2} = u^{2} + 2gs }[/tex]
Subsitute the required values,
[tex]\sf{ v^{2} = 0^{2} + 2{\times}9.8{\times}45 }[/tex]
[tex]\sf{ v^{2} = 90{\times}9.8}[/tex]
[tex]\sf{ v^{2} = 882 m}[/tex]
[tex]\sf{ v = \sqrt{882} m}[/tex]
[tex]\sf{ v = 29.7 m/s}[/tex]
Hence, The final velocity of the stone when the stone hits the ground is 29.7 m.
