zarookrigi6
Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Two trains (A and B) are travelling on two parallel rails to the same direction. Train A
which was at rest starts to travel with an acceleration of 0.5ms² from the station X. Train
B passes A with a velocity of 15 ms when A starts to travel.
(a) Draw velocity-time graphs using the same axis to the motion of the trains.
(b) If both the trains are having same velocity at t₁ and displacement at t2, find t; and
12.
(c) If both the trains meet at the station Y, what is the distance from X to Y?


​

Sagot :

MathPhys

Answer:

(a) See graph.

(b) t₁ = 30 s, and t₂ = 60 s

(c) d = 900 m

Explanation:

Acceleration (a) is the change in velocity (v) over time (t). An object with constant acceleration will have a linear increase in velocity over time, where the slope of the line is the acceleration. The displacement of the object is equal to the area under the velocity-time curve.

Part A: Velocity-Time Graphs

Train A has a constant acceleration of a = 0.5 m/s² and an initial velocity of u = 0 m/s. Its velocity as a function of time is therefore:

v = u + at

v = (0 m/s) + (0.5 m/s²) t

v = 0.5t

Train B has a constant velocity of 15 m/s. Its velocity as a function of time is therefore:

v = 15

Part B: Equal Velocity and Displacement

When the velocities are equal, the time is:

0.5t₁ = 15

t₁ = 30 s

The displacement is the area under the curve. For train A, the area is a triangle, with width t₂ and height 0.5t₂. For train B, the area is a rectangle, with width t₂ and height 15. When the displacements are equal, the time is:

½ (t₂) (0.5t₂) = (t₂) (15)

0.25 t₂ = 15

t₂ = 60 s

Part C: Distance from X to Y

The distance between the two stations is equal to the displacement at t₂.

d = (60) (15)

d = 900 m

View image MathPhys
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.