A force of 10N acts on a body of mass 10kg. As a result, the body covers 100cm in 4 seconds, moving along a straight line. Find the initial velocity.
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Answers
Required Answer :
The initial velocity of the body = - 1.75 m/s
Given :
- Force acting on a body = 10 N
- Mass of a body = 10 kg
- Distance covered by the body = 100 cm
- Time taken by the body = 4 seconds
To find :
- Initial velocity of the body
Solution :
Firstly, we will calculate the acceleration of the body by using the formula of force.
Formula of force :
- F = ma
where,
- F denotes the force
- m denotes the mass
- a denotes the acceleration
Substituting the given values :
→ 10 = 10 × a
→ 10/10 = a
→ 1 = a
Acceleration of the body = 1 m/s²
To calculate the initial velocity of the body we will use the second equation of motion.
Second equation of motion :
- s = ut + ½ at²
where,
- s denotes the distance
- u denotes the initial velocity
- a denotes the acceleration
- t denotes the time
we have,
- s = 100 cm
- a = 1 m/s²
- t = 4 seconds
Distance is given in cm, so firstly we will convert the distance from cm into m.
As we know,
- 1 m = 100 cm
So, to convert the value from cm into m, divide it by 100.
→ Distance = 100/100
→ Distance 1 m
Substituting the given values :
→ 1 = (u)(4) + ½ (1)(4)²
→ 1 = 4u + ½ × 4 × 4
→ 1 = 4u + 2 × 4
→ 1 = 4u + 8
→ 1 = 4u + 8
→ 1 - 8 = 4u
→ - 7 = 4u
→ - 7/4 = u
→ - 1.75 = u
Therefore, the initial velocity of the body = - 1.75 m/s
The initial velocity is negative because it is acting in the opposite direction.