Two cars are traveling along a straight line in the same direction, the lead car

Question

Two cars are traveling along a straight line in the same direction, the lead car at 25.2m/s and the other car at 29.2m/s. At the moment the cars are 39.6m apart, the lead driver applies the brakes, causing her car to have an acceleration of -2.01m/s2. How long does it take for the lead car to stop?What is the distance it travels during this time?Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing car's minimum negative acceleration so as not to hit the lead car?How long does it take for the chasing car to stop?

Explanation / Answer

here,

speed of the leading car , u1 = 25.2 m/s

deaccelration , a = - 2.01 m/s^2

let the time taken to stop be t1

v = 0 = u1 + a1 * t1

0 = 25.2 - * 2.01 * t1

t1 = 12.54 s

the time taken to stop the leading car is 12.54 s

let the distance be s1

s1 = u1 * t1 + 0.5 * a1 * t1^2

s1 = 25.2 * 12.54 - 0.5 * 2.01 * 12.54^2

s1 = 157.97 m

let the chasing car minimum negative accelration be a2

safety distance , s2 = s1 + 39.6 m

s2 = 157.97 + 39.6

from third equation of motion

v2^2 - u2^2 = 2 * a2 * s2

0 - 29.2^2 = 2 * a2 * 197.57

a2 = 2.16 m/s^2

the minimum negative accelration is 2.16 m/s^2

let the time taken to stop be t2

v2 = u2 + a2 * t2

0 = 29.2 - 2.16 * t2

t2 = 13.53 s

the time taken for chasing car is 13.53 s

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