A red train traveling at 72 km/hand a green train traveling at 144km/hare headed toward each other along a straight, level track. When they are 950 mapart, each engineer sees the other’s train and applies the brakes. The brakes slow each train at the rate of1.0m/s2 . Is there a collision? If so, answer yes, give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

Short Answer

Expert verified

(a) Yes, trains will collide.

(b) When the trains collide, the speed of the red train is 0m/sand the speed of the green train is 10m/s

Step by step solution

01

Given data

The speed of a red train, v0r=72km/h.

The speed of a green train,v0g=144km/h

The separation between the two trains is 950 m.

The rate at which the speed is decreased,a=1.0m/s2

02

Kinematic Equations of Motion

Kinematics is the study of how a system of bodies moves without taking into account the forces or potential fields that influence motion. The equations which are used in the study are known as kinematic equations of motion. The kinematic equations relate the velocity, displacement, acceleration, and time to each other.

03

(a) Determination of the collision

The final velocity of both trains is zero for the calculation of distance travelled by them before stopping. Using the kinematic equation, For the red train:

v=v0r+at

(i)

t=v-v0a=0m/s-20m/s-1m/s2=20s

The distance traveled by the red train is calculated as,

x=v0rt+12×-1m/s220s2=200m

Time taken by green train to come to rest,

t=v-v0a

Distance travelled by the green train is calculated as,

x=v0t+12at2=40m/s×40s+12×-1m/s240s2=800m

Thus, total distance travelled is 200m+800m=1000m,but given separation is 950 m.

This shows that trains will collide.

04

(b) Calculation for the speed for the green train

The speed of the red train is zero as it travels a distance of 200 m and then stops. The green train moves with speed and travels a distance of 750 m and collides with the red train.

Use the kinematic equation to find the speed of the green train.

V2=40m/s2+2-1m/s2750m=100m2/s2v=10m/s

Thus, the speed of the green train while colliding is, 10m/s.

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