Please show every step in the solutions for the problems! Many thanks in advance

Question

Please show every step in the solutions for the problems! Many thanks in advance!

Two trains start 5 minutes apart. Starting from rest, each is capable of a maximum speed of 300 km/h after uniformly accelerating over a distance of 4 km. (a) What is the acceleration of each train? (b) How far is the first train ahead when the second one starts? (c) How far apart are they when they are both traveling at maximum speed? A rocket is fired vertically upward with an initial velocity of 80 m/s. It accelerates upward at 4 m/s2 until it reaches an altitude of 1000 m when its engines fail and it is influenced only by the Earth's gravity, (a) How long is the rocket in motion? (b) What is its maximum altitude? (c) What is its velocity just before it crashes back into the Earth? A commuter train travels between two stations by accelerating at a rate a for a time t1 and then slowing down with a negative acceleration of -5a for a time t?. The two stations are a distance d apart and the train never reaches its maximum speed. The train stops at each station. Find the times t1 and t2. A stone is thrown upwards from the edge of a cliff 18 m high. It just misses the cliff on the way down and hits the ground below with a speed of 25 m/s. (a) With what velocity was it released? (b) What is its maximum height above the edge of the cliff?

Explanation / Answer

answer 1

a> acceleration = v2/2s = 300*300/2*4 = 11250 km/hr2

b> time taken to reach max speed = 60*300/11250 min = 1.6 min

distance covered = 4 km

distance covered in next (5-1.6) min = 3.4*300/60 = 17 km

? 1st train is 21 km ahead!

c> distance covered by train to reah max speed = 4 km

distance covered by 1st train in this interval= 1.6*300/60 = 8 km

? 1st train is 25 km ahead!

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