Question

A train is traveling up a 2.78 ∘ incline at a speed of 4.31 m/s when the last car breaks free and begins to coast without friction.

A)How long does it take for the last car to come to rest momentarily?

B) How far did the last car travel before momentarily coming to rest?

Answer 1

A)

consider the motion parallel to incline

= angle of the incline = 2.78 deg

g = acceleration due to gravity in down direction = 9.8 m/s²

a = acceleration of the train parallel to incline oppsoite to direction of motion = - g Sin = - (9.8) Sin2.78

a = - 0.48 m/s²

v_o = initial velocity of train at the bottom of incline = 4.31 m/s

v = final velocity of train as it comes to stop = 0 m/s

Using the kinematics equation

v = v_o + a t

0 = 4.31 + (- 0.48) t

t = 8.98 sec

b)

d = stopping distance travelled parallel to incline before coming to stop

Using the equation

v² = v_o² + 2 a d

0² = 4.31² + 2 (- 0.48) d

d = 19.4 m