An object of mass 2 kg moves from rest when a force of 5 N is applied for 10 s.
a. Calculate the acceleration of the object ?
b.What is the velocity of the object after 10 seconds ?
c. Calculate the amount of work done ?
Answers
Answer :
- Acceleration of the object, a = 2.5 m/s²
- Velocity of the object after 10 seconds, v = 25 m/s
- Amount of work done by the body, W = 625 J
Explanation :
Given :
- Mass of the object, m = 2 kg
- Force acting on the object, F = 5 N
- Time of contact of force, t = 10 s
- Initial velocity of the object, u = 0 m/s
[Initial velocity is taken as zero because the object is starting from rest]
To find :
- Acceleration of the object, a = ?
- Velocity of the object after 10 seconds, v = ?
- Amount of work done by the body, W = ?
Knowledge required :
- Formula for force applied by a body :
⠀⠀⠀⠀⠀⠀⠀⠀⠀F = ma⠀
⠀[Where : F = Force applied by the body, m = Mass of the body, a = Acceleration produced by the body]
- First equation of motion :
⠀⠀⠀⠀⠀⠀⠀⠀⠀v = u + at⠀
⠀[Where : v = Final Velocity of the body, u = Initial velocity of the body, a = Acceleration produced by the body, t = Time taken]
- Second equation of motion :
⠀⠀⠀⠀⠀⠀⠀⠀⠀s = ut + ½at²⠀
⠀[Where : s = Distance traveled by the body, u = Initial velocity of the body, a = Acceleration produced by the body, t = Time taken]
- Formula for work done by a body ;
⠀⠀⠀⠀⠀⠀⠀⠀⠀W = F s⠀
⠀[Where : W = Work done of the body, F = Force applied on the body, s = Displacement of the body]
Solution :
To find out the acceleration produced by the body :
⠀By using the equation for force and substituting the values in it, we get :
⠀⠀=> F = ma
⠀⠀=> 5 = 2 × a
⠀⠀=> 5/2 = a
⠀⠀=> 2.5 = a
⠀⠀⠀⠀⠀∴ a = 2.5 m/s²
Hence the accelaration produced by the body is 2.5 m/s².
To find out the velocity of the body after 10 s :
⠀By using the first equation of motion and substituting the values in it, we get :
⠀⠀=> v = u + at
⠀⠀=> v = 0 + 2.5 × 10
⠀⠀=> v = 25
⠀⠀⠀⠀⠀∴ v = 25 m/s
Hence the velocity of the body after 10 s is 25 m/s.
To find out the displacement the body :
⠀By using the second equation of motion and substituting the values in it, we get :
⠀⠀=> s = ut + ½at²
⠀⠀=> s = (0)10 + ½ × 2.5 × 10²
⠀⠀=> s = ½ × 2.5 × 100
⠀⠀=> s = 125
⠀⠀⠀⠀⠀∴ s = 125 m
Hence the displacement of the body is 125 m.
To find out the work done by the body :
⠀By using the formula for work done on a body and substituting the values in it, we get :
⠀⠀=> W = F s
⠀⠀=> W = 5 × 125
⠀⠀=> W = 625
⠀⠀⠀⠀⠀∴ W = 625 J
Hence the work done by the body is 625 J.
Force = mass × acceleration (Law of inertia or Newton's first law of motion)
Force = 5 Newton
Mass = 2 Kilogram
5 = 2a
Acceleration = 2.5 metres/second square or mps^2
Final Velocity = Initial Velocity + (acceleration × time)
v = 0 + 2.5×10
Final Velocity = 25 metres per second or mps
Work = Force × Displacement
Displacement = (Initial Velocity × time) + (0.5 × acceleration × time × time)
W = 5 × [ ( 0 × 10 ) + ( 0.5 × 2.5 × 10 × 10 ) ]
W = 5 × [ 125 ]
Work = 625 Joules
:-)