A force of 2i+7jN acts on a body of mass 5kg for 10 seconds. The body was initally moving with constant velocity of i-2jm/s.Find the final velocity of the body in m/s, in vector form. (a)5i+12j(b)12i-5j(c)10i-7j(d)7i+10j
Use the kinematics equation:
Vf=Vi+at
where
Vf=final velocity=i-2j (m/s)
Vi=initial velocity, yet unknown
a=acceleration=F/m (in vector form)
t=time=10 s
a=(2i+7j)/5=0.4i + 1.4j
Vf=(i-2j)+(0.4i+1.4j)(10)
=(i-2j)+(4i+14j)
=5i+12j
To find the final velocity of the body, we can use Newton's second law of motion. According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Force = 2i + 7j N
Mass = 5 kg
Time = 10 seconds
Initial velocity = i - 2j m/s
First, we need to find the acceleration of the body. We can use Newton's second law to calculate the acceleration.
Force = Mass * Acceleration
Acceleration = Force / Mass
Acceleration = (2i + 7j N) / 5 kg
Acceleration = (2/5)i + (7/5)j m/s²
Next, we need to find the change in velocity using the formula:
Change in Velocity = Acceleration * Time
Change in Velocity = [(2/5)i + (7/5)j m/s²] * 10 s
Change in Velocity = 2i + 7j m/s
To find the final velocity, we add the change in velocity to the initial velocity:
Final Velocity = Initial velocity + Change in Velocity
Final Velocity = (i - 2j m/s) + (2i + 7j m/s)
Final Velocity = (1 + 2)i + (-2 + 7)j
Final Velocity = 3i + 5j
Therefore, the final velocity of the body in vector form is 3i + 5j m/s.
The correct answer is (d) 3i + 5j.