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A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required. - CBSE Class 9 - Science

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Question

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

Solution

Mass of the motor car, m = 1200 kg

Initial velocity of the motor car, u = 90 km/h = 25 m/s

Final velocity of the motor car, v = 18 km/h = 5 m/s

Time taken, = 4 s

According to the first equation of motion:

v = u + at

5 = 25 + a (4)

a = − 5 m/s2
Negative sign indicates that its a retarding motion i.e. velocity is decreasing.

Change in momentum = mv − mu = m (vu)

= 1200 (5 − 25) = − 24000 kg m s−1

Force = Mass × Acceleration

= 1200 × − 5 = − 6000 N

Acceleration of the motor car = − 5 m/s2

Change in momentum of the motor car = − 24000 kg m s−1

Hence, the force required to decrease the velocity is 6000 N.
(Negative sign indicates retardation, decrease in momentum and retarding force)

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Science Textbook for Class 9 (2018 to Current)
Chapter 9: Force and Laws of Motion
Q: 4 | Page no. 130
Solution A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required. Concept: Mathematical Formulation of Second Law of Motion.
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