Answer:
Given :-
- A vehicle of mass 20 kg is moving with a velocity of 4 m/s .
- If it is applied on the vehicle so that the vehicle of 1 m/s after travelling a distance of 20 m.
To Find :-
- What is the magnitude of the force.
Solution :-
First, we have to find the acceleration :-
Given :
- Initial Velocity (u) = 4 m/s
- Final Velocity (v) = 1 m/s
- Distance Covered (s) = 20 m
According to the question by using the formula we get,
[tex]\implies \sf\boxed{\bold{v^2 =\: u^2 + 2as}}\\[/tex]
[tex]\implies \sf (1)^2 =\: (4)^2 + 2a \times 20\\[/tex]
[tex]\implies \sf (1 \times 1) =\: (4 \times 4) + 40a\\[/tex]
[tex]\implies \sf 1 =\: 16 + 40a\\[/tex]
[tex]\implies \sf 1 - 16 =\: 40a\\[/tex]
[tex]\implies \sf - 15 =\: 40a\\[/tex]
[tex]\implies \sf \dfrac{- 15}{40} =\: a\\[/tex]
[tex]\implies \sf - 0.375 =\: a\\[/tex]
[tex]\implies \sf\bold{a =\: - 0.375\: m/s^2}\\[/tex]
Hence, the acceleration is - 0.375 m/s² .
Now, we have to find the magnitude of the force :-
Given :
- Mass (m) = 20 kg
- Acceleration (a) = - 0.375 m/s²
According to the question by using the formula we get,
[tex]\implies \sf\boxed{\bold{Force =\: Mass \times Acceleration}}\\[/tex]
[tex]\implies \sf Force =\: 20 \times (- 0.375)\\[/tex]
[tex]\implies \sf Force =\: - 7.5\\[/tex]
[tex]\implies \sf\bold{\underline{Force =\: - 7.5\: N}}\\[/tex]
[tex]\therefore[/tex] The magnitude of the force is - 7.5 N .