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Question

A motorcar of mass 1200kg is moving along a straight line with a uniform velocity of 90km/h. Its velocity is slowed down to 18km/h in 4s by an unbalanced external force. calculate the acceleration and change in momentum. also, calculate the magnitude of the force required.


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Solution

Step 1: Given data.

  1. The mass of the motorcar is 1200kg.
  2. The initial velocity of the car is 90km/h.
  3. The final velocity of the care is 18km/h.
  4. The time of acceleration is 4s.

Step 2: Concept and formula to be used.

  1. The formula of momentum p is mass m multiplies by velocity v, that is p=mv.
  2. The change in momentum p is given by final momentum p2 minus initial momentum p1, that is p=p2-p1.
  3. According to the equation of motion, v=u+at.
  4. The magnitude of the force is given by F=ma.

Step 3: Find the acceleration of the motorcar.

Since the motorcar slowed down from 90km/h to 18km/h in 4s.

So, the initial speed is 90km/h, the final speed is 18km/h and the time is 4s.

Convert the speed in m/s.

So, 90km/h is equal to 25m/s and 18km/h is equal to 5m/s

So, the acceleration a of the motorcar is given by:

5=25+4a4a=-20a=-5

Therefore, the acceleration of the motorcar is -5m/s2.

Step 4: Find the change in momentum of the motorcar.

Since, the mass of the motorcar is 1200kg and the initial velocity is 25m/s.

So, the initial momentum p1 is given by:

p1=1200·25p1=30000

Since, the final velocity is 5m/s.

So, the final momentum p2 is given by:

p2=1200·5p2=6000

So, the change in momentum p is given by:

p=6000-30000p=-24000

Therefore, the change in momentum is -24000kg·m/s.

Step 5: Find the magnitude of the required force.

Since, the mass of the motorcar is 1200kg and the acceleration is -5m/s2.

So, the magnitude of the force F is given by:

F=1200·-5F=6000

Therefore, the magnitude of the required force is 6000N.

Hence, the acceleration, change in momentum and the magnitude of the force required are -5m/s2, -24000kg·m/s and 6000N respectively.


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