Answer:
Final velocity, V = 2.1213 m/s.
Explanation:
Given the following data;
Force, F = 1.50N
Mass, m = 0.2kg
Displacement, S = 30cm to meters = 30/100 = 0.3m
To find the acceleration;
Force is given by the multiplication of mass and acceleration.
Mathematically, Force is given by the formula;
[tex] F = ma[/tex] .......equation 1
Where;
- m represents the mass of an object.
- a represents acceleration.
Making acceleration (a) the subject, we have;
[tex]Acceleration (a) = \frac{F}{m}[/tex]
Substituting into the above equation, we have;
[tex]Acceleration, a = \frac{1.5}{0.2}[/tex]
Acceleration, a = 7.5m/s²
Now to find the final velocity, we would use the third equation of motion;
[tex] V^{2} = U^{2} + 2aS [/tex] .....equation 2
Where;
- V represents the final velocity measured in meter per seconds.
- U represents the initial velocity measured in meter per seconds.
- a represents acceleration measured in meters per seconds square.
- S represents the displacement measured in meters.
Note: Since the trolley is starting from rest, we know that it's initial velocity is 0.
Substituting the values into equation 2, we have;
[tex] V^{2} = 0^{2} + 2*7.5*0.3[/tex]
[tex] V^{2} = 0 + 4.5[/tex]
[tex] V^{2} = 4.5[/tex]
Taking the square root, we have;
[tex] V = \sqrt {4.5}[/tex]
V = 2.1213 m/s.
Therefore, the speed of the trolley after accelerating from rest through 0.3 m, if friction is negligible is 2.1213 m/s.
