A subway train starts from rest at a station accelerates at rate of 1.60 m/s^2 f

Question

A subway train starts from rest at a station accelerates at rate of 1.60 m/s^2 for 14.0 s. It runs at a constant speed for 70.0 s and slows down at a rate of 3.50 m/s2 until it stops at the next station. Find the distance between the train stations. You're driving down the highway late one night at 16.0 m/s when a deer steps onto the road 39.0 M in front of you. Your reaction time before stepping on the breaks is 0.50 s, and the maximum deceleration of your car is 12.0 m/s^2. How much distance is in between you and the deer when you come to a stop? What is the maximum speed you could have and still not hit the dear? Make sure you follow the steps below: Read the whole problem and make sure you understand it. Then read it again. Decide on the objects under study and what the time interval is. Choose coordinate axis and draw a diagram. Write down the known (given) quantities, and then the unknown ones that you need to find. What physics applies here? Plan an approach to a solution Which equations relate the known and unknown quantities? Are they valid in this situation? Solve algebraically for the unknown quantities, and check that your result is sensible (correct dimensions).

Explanation / Answer

here,

1)

for accelrating phase

a1 = 1.6 m/s^2

t1 = 14 s

the first displacement , d1 = 0 + 0.5 * a1 * t1^2

d1 = 0 + 0.5 * 1.6 * 14^2

d1 = 156.8 m

for constant speed

v1 = u + a1 * t1 = 22.4 m/s

t2 = 70 s

d2 = v1 * t2 = 1568 m

for deaccelrting phase

0^2 - v1^2 = - 2 * a2 * d3

0 - 22.4^2 = - 2 * 3.5 * d3

d3 = 71.68 m

the distance between stations , d = d1 + d2 + d3

d = 1796.5 m

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