NCERT Solutions Class 9 Science Solutions for Additional Exercises 2 in Chapter 9 - Force and Laws of Motion
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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.
Given, mass of the car (m) = 1200kg
Initial velocity (u) = 90 km/hour = 25 meters/sec
Terminal velocity (v) = 18 km/hour = 5 meters/sec
Time period (t) = 4 seconds
\text { The acceleration of the car can be calculated with the help of the formula: } a=\frac{v-u}{t}
a=\frac{5-25}{4} m . s^{-2}=-5 \mathrm{ms}^{-2}
\text { Therefore, the acceleration of the car is }-5 \mathrm{ms}^{-2}
Initial momentum of the car = m × u = (1200kg) × (25m/s) = 30,000 kg.m.s^{-1}
Final momentum of the car = m × v = (1200kg) × (5m/s) = 6,000 kg.m.s^{-1}
Therefore, change in momentum (final momentum – initial momentum) = (6,000 – 30,000) kg.m.s^{-1}
= -24,000 kg.m.s^{-1}
External force applied = mass of car × acceleration
= (1200kg) × (-5 ms^{-2}) = -6000N
Therefore, the magnitude of force required to slow down the vehicle to 18 km/hour is 6000 N
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