A subway train travels between two stations that are separated by 1800 m. It doe

Question

A subway train travels between two stations that are separated by 1800 m. It does this in three segments. First, it starts from rest and accelerates at a rate of 1.60 m/s2 for 14.0 s. It then continues at a constant speed for 70.0 s. Finally, it slows down so that it stops when it reaches the second station. What is the required acceleration for the last segment? (Ans: -3.35 m/s^2) A ball is launched upward with an unknown initial velocity. When it has moved up 15.0 m, it has an upward speed of 18.0 m/s. Find the ball's initial velocity, the highest point the ball reaches above its launch location, and the time from launch until the ball returns to its launch location. Assume freefall conditions for this problem so that |g| = 9.8 m/s^2. (Ans: 24.9 m/s, 31.6 m, 5.08 s) Two cars start 30.0 m apart and move towards each other. One starts from rest while the other one starts with a speed of 10.0 m/s. The car starting from rest speeds up at a rate of 3.00 m/s each second while the other car slows down at a rate of 2.00 m/s each second. What is the speed of each car when they collide? (Ans: 7.95 m/s, 4.70 m/s)

Explanation / Answer

for first 14sec,

d = u t + a t^2 /2

d1 = 0 + (1.60 x 14^2)/2 = 156.8 m

speed after 14 sec,

v = u + a t

v1 = 0 + (1.60 x 14) = 22.4 m/s

after that dor 70s,

d2 = (22.4 x 70) + (0) = 1568 m

now its speed is 22.4 m/s

and distance have to travel in last segment = 1800 - d1 - d2 = 75.2 m

as it finally stops hence vf = 0

vf^2 - vi^2 = 2 a d

0^2 - 22.4^2 = 2 (a) (75.2)

a = - 3.34 m/s^2

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