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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.

Q A4.     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.

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The initial and final velocities are :

$u\ =\ 90\times \frac{5}{18}\ =\ 25\ m/s$

and                                                    $v\ =\ 18\times \frac{5}{18}\ =\ 5\ m/s$

Using equation of motion we can write :

$v\ =\ u\ +\ at$

or                                                $5\ =\ 25\ +\ a\times 4$

or                                                $a\ =\ -5\ m/s^2$

Now the force is given by :

$F\ =\ ma$

or                                                    $=\ 1200\times (-5)\ =\ -\ 6000\ N$

And the change in momentum is :           $\Delta p\ =\ m\Delta v$

or                                                                       $=\ 1200(-20)\ =\ - 24000\ Kg\ m/s$

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