The driver of a 2.0 × 103 kg red car traveling on the highway at 45m/s slams on his brakes to avoid striking a second yellow car in front of him, which had come to rest because of blocking ahead as shown in above Fig. After the brakes are applied, a constant friction force of 7.5 × 103 N acts on the car. Ignore air resistance.
(a) Determine the least distance should the brakes be applied to avoid a collision with the other vehicle?
(b) If the distance between the vehicles is initially only 40.0 m, at what speed would the collision occur?
(c) Write your conclusive observations on the result obtained from this numerical. i.e. the importance of Physics in daily life.
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Answer:
Explanation:
Initial speed of the car A u=52 kmh
−1
=52×
18
5
=14.44 ms
−1
The car stops in 5 seconds i.e v=0 at t=5
(A) : Initial speed of the car A u=3 kmh
−1
=3×
18
5
=0.83 ms
−1
The car stops in 10 seconds i.e v=0 at t=10
With the help of these initial and final points for both the cases, we can plot the graph of speed vs time.
Area under the speed-time graph gives the distance covered.
∴ Distance covered by car A x
A
=
2
1
×14.44×5=36.1 m
∴ Distance covered by car A x
B
=
2
1
×0.83×10=4.15 m
Thus car A travels more distance than B.
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