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Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If
Question
Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If car B travels a distance D before stopping, how far does car A travel before stopping?
A) 4D
B) 2D
C) D
D) D/2
E) D/4
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Physics
3 years
2021-08-31T18:50:01+00:00
2021-08-31T18:50:01+00:00 1 Answers
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Answers ( )
Answer:
A) 4D
Explanation:
The distance traveled by the cars before coming to rest can be determined by 3rd equation of motion:
2as = Vf² – Vi²
s = (Vf² – Vi²)/2a
where,
s = distance traveled
Vf = Final Speed = 0 m/s
Vi = Initial Speed
a = deceleration rate
First, we consider Car B and we assign a subscript 2 for it:
Vf₂ = 0 m/s (As, car finally stops)
s₂ = D
a₂ = – a (due to deceleration)
D = (0² – Vi₂²) /(-2a)
D = Vi₂²/2a ——– equation (1)
Now, we consider Car A and we assign a subscript 1 for it:
Vf₁ = 0 m/s (As, car finally stops)
s₁ = ?
a₁ = – a (due to deceleration)
Vi₁ = 2 Vi₂ (Since, car A was initially traveling at twice speed of car B)
s₁ = (0² – Vi₁²) /(-2a)
s₁ = (2Vi₂)²/2a
s₁ = 4 (Vi₂²/2a)
using equation (1), we get:
s₁ = 4D
Therefore, the correct option is:
A) 4D