The time taken by the jogger to jog from point A to Point B is 2 seconds.
Option B) 2.0s is the correct answer.
Given the data in the question;
- Distance from point A to point B; [tex]s = 5.0m[/tex]
- Initial velocity or speed; [tex]u = 2.0m/s[/tex]
- Final velocity; [tex]v = 3.0m/s[/tex]
- Time taken to reach B from A; [tex]t = \ ?[/tex]
First we find the acceleration of the jogger, using the Third Equation of Motion:
[tex]v^2 = u^2 + 2as[/tex]
Where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance travelled.
So we substitute our values into the equation
[tex](3.0m/s)^2 = ( 2.0m/s)^2 \ +\ ( 2\ *\ a\ *\ 5.0m)\\\\9m^2/s^2 = 4m^2/s^2 \ +\ (10m \ * \ a)\\\\a = \frac{9m^2/s^2\ -\ 4m^2/s^2}{10m} \\\\a = \frac{5m^2/s^2}{10m} \\\\a = 0.5m/s^2[/tex]
Now, we calculate the time it took the jogger to reach B from A.
From the First Equation of Motion:
[tex]v = u + at[/tex]
Where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time.
We make time "t", the subject of the formula
[tex]t = \frac{v -u}{a}[/tex]
We substitute our values into the equation
[tex]t = \frac{3.0m/s\ - \ 2.0m/s}{0.5m/s^2} \\\\t = \frac{1.0m/s}{0.5m/s^2}\\\\t = 2s[/tex]
Therefore, the time taken by the jogger to jog from point A to Point B is 2 seconds.
Option B) 2.0s is the correct answer.
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