Question

At 4:11 p.m. in the highway and at the height of town, a police patrol was traveling at a speed of 18.0 m / s, when the citizen's car approaches a speed of 94 mi / h towards . After a reaction time of 0.800 seconds, the police start chasing the citizen with an acceleration of 5.00 m / s2. Including the reaction time: (a) How long does it take for the police patrol to reach the citizen? (b) Indicate how far it reaches, from the moment the persecution begins, and create a Position vs. time graph, showing the two movements (that of the citizen and that of the police patrol)

Answer 1

94 mi/h = 42.0218 m/s

Let distance traveled by speeding car be x, then

x = 42.0218 * t

distance traveled by police car in reaction time

d = 18 * 0.8 = 14.4 m

so, police catches the speeding car after a distance of x - 14.4 in time t - 0.8

so,

x - 14.4 = 18 * (t - 0.8) + 1/2 * 5 * (t - 0.8)²

42.0218 * t - 14.4 = 18 *t - 14.4 + 1/2 * 5 * (t²  + 0.64 - 1.6t)

42.0218 * t = 18 * t + 2.5 * t² + 1.6 - 4 * t

2.5 * t² - 28.0218 * t + 1.6 = 0

solve this, I got

t = 28.0218 +/- 27.734 / 5

t = 11.15 seconds

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here, we don't consider reaction time as question asks after persecution begins

so,

x = 18 * 10.35 + 1/2 * 5 * (10.35)²

x = 454.17 m

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