A bank robber traveling at 75 mi/hr in an escape car suddenly sees a barricade 1

Question

A bank robber traveling at 75 mi/hr in an escape car suddenly sees a barricade 150 meters ahead. The robber slams on the brakes following a 0.75 second delay (the drivers reactiong time). After the brakes are applied, the car deaccelerates at 4.0 m/s^2. Will the car hit the barricade? Use bot 1D kinematics and forces to solve this problem.

1) Draw a meaningful sketch of this problem.

2)Identify and label the known quantities on your sketch.

3)What is the question being asked?

4) Which of the five principles of motion equations would be most helpful at solving this equation?

5)Solve this problem and draw a conclusion on the answer. (e.g. Does it make sense)

Explanation / Answer

1-2-3)

for the reaction time, car will travel with constant initial speed and itwill travel some ditance.

and after brakes are slammed then speed of car start decreasing.

if car stops before this remaining distance between car and barricade. thencar will not hit .

if car is still moving then car will hit barricade.

5) for reaction time (0.75 s), car will travel with 75 mi/hr.

vi = 75 mi/hr = 75 x 1609 m / 3600s = 33.52 m/s

distance traveled in this time = vi *t = 33.53 x 0.75 = 25.14 m

now remaining distane, d = 150 - 25.14 = 124.86 m

now a = - 4 m/s^2

lets after what time speed will become zero.

Applying

vf = vi + at

0 = 33.53 + (-4 t )

t = 8.38 sec

distance traveled in this time. d = vi*t + a t^2 /2

d = (33.53 x 8.38) + (-4 x 8.38^2 /2 ) = 140.45 m

but remaining distance is 124.86 m

hence car will hit barricade.

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