When a high-speed passenger train traveling at v P = 121 km/h rounds a bend, the

Question

When a high-speed passenger train traveling at vP = 121 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 700 m ahead. The locomotive is moving at vL = 26 km/h. The engineer of the passenger train immediately applies the brakes. Assume that an x axis extends in the direction of motion. What must be the constant acceleration along that axis if a collision is to be just avoided?

Please also convert final answer to m/s^2. Thank you!

Explanation / Answer

Here we will use 3 main equation:

S= uT + 1/2*a*T2

v2- u2 = 2 * a * s

v= u + aT

Let vT = initial velocity of train

vL = locomotive velocity

the final velocity of train should be vL to avoid the collision.

(vT+vL)/2 = (D + vL*T) / T = D/T + vL

using v= u + aT for T

we get

(vT+vL)/2 = D /(vL-vT)/a + vL

hence solving we get

a = -1/2D * (vL - vt)2

= - 0.5/0.700 * (26-121)2 = 6446.4 km/h2 = 0.497 m/s2 = 0.50 m/s2(approx)

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