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Naya [18.7K]
3 years ago
6

A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. what minimum constant decele

ration is required to stop the car in time to avoid a pileup? (round your answer to two decimal places.)
Physics
1 answer:
Effectus [21]3 years ago
4 0
Assuming the driver starts slamming the brakes immediately, the car moves by uniformly decelerated motion, so we can use the following relationship
2aS = v_f^2 - v_i^2 (1)
where 
a is the deleceration
S is the distance covered after a time t
v_f is the velocity at time t
v_i=100 km/h = 27.8 m/s is the initial speed of the car

The accident is 80 m ahead of the car, so the minimum deceleration required to avoid the accident is the value of a such that S=80 m and v_f=0 (the car should stop exactly at S=80 m to avoid the accident). Using these data, we can solve  the equation (1) to find a:
a=- \frac{v_i^2}{2 S}= -\frac{(27.8 m/s)^2}{2 \cdot 80 m} =-4.83 m/s^2
And the negative sign means it is a deceleration.

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