Speed and Velocity Solved

1) Two trains, one traveling at 68km/h and the other at 136km/h. They are headed toward one another along a straight level track. When they are 867m apart each engineer sees the other's train and applies brakes. The brakes decelerates each train at the rate of 1.0m/s^2. Is there a collision?

a) Yes b) No
b) What distance do the trains need to allow between them to stop at this acceleration?
c) What acceleration do the two trains need to have to stop exactly in a distance of 867m?

2) A ball is thrown vertically upwards with an initial velocity of 27m/s. No air resistance, how long is the ball in the air?
a) What is the greatest height reached by the ball?
b) Calculate the first time where the ball has half of its initial velocity.

3) A stone is thrown vertically upward at a speed of 38.40m/s at time t=0. A second stone is thrown upward with the same speed 3.410 seconds later. At what time are the two stones at the same height?
a) At what height do the two stones pass each other?
b) What is the downward speed of the first stone as they pass each other?

4) To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 23km/h approaches a car stopped at the red light. When the truck is 97.6 meters from the car the light turns green and the car immediately begins to accelerate at 2.8m/s^2. How close does the truck come to the car assuming the truck does not slow down?
a) How far from the stop light has the car traveled when the truck reaches its closet distance?