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A car is travelling in a straight line at 20 m/s when the driver sees a cat dart into the road and jams on the brakes. The car comes to a complete stop in 4.0 s. If the mass of the car and driver is 1,800 kg, what is the magnitude of the braking force that slows down and stops the car?100 N450 N36,000 N9,000 N

Answer :

The breaking force is 9000 N.

Given data:

• The initial velocity of car is u=20 m/s

,

• Time taken for compelete stop is t=4.0 s.

,

• The mass of the car is m=1800 kg.

The car finally stops; therefore, the final velocity of car is v=0 m/s.

Applying the kinematic equation to calculate the acceleration of the car as,

[tex]\begin{gathered} v=u+at \\ 0=20+a(4) \\ a=-5\text{ m/s}^2 \end{gathered}[/tex]

Here, negative sign of acceleration indicates that the acceleration is acting in opposite direction.

The breaking force can be calculated by Newton's second law as,

[tex]\begin{gathered} F=ma \\ F=(1800)(5) \\ F=9000\text{ N} \end{gathered}[/tex]

Thus, the breaking force is 9000 N.

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