Question

4. A train started from a station and accelerated at 0.5 ms-2 to reach its top speed of 50 m s-1 and maintained this speed for 90 minutes. As the train approached the next station the driver applied the brakes uniformly to bring the train to a stop in a distance of 500 m.

a) Calculate how long it took the train to reach its top speed.
b) Calculate the acceleration experienced by the train when the brakes were applied.​

Answer 1

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a) As the train approached the next station the driver applied the brakes uniformly to bring the train to a stop in a distance of 500 m.

-» (i)v=u+at

• 50 = 0) + 0.50

• t=50/0.5 = 100 s

(i)s=ut + ½ at² (but a = 0)

• s=50x (90x60) = 270000 m

(i)v²=u² + 2as

. 0=50² + 2a(500)

• a=-2500/1000 = -2.5 mst

b) Calculate how long it took the train to reach its top speed.

-» • A car is travelling at a velocity of 25 m s² when the engine is then turned off; calculate how far the car will travel before coming to rest if the deceleration is 1.47 ms ²?

• v² = u ² + 2as

• 0 = 25 +2(-1.47) s or s = $\: \fbox\pink{213 m}$

b) Calculate the acceleration experienced by the train when the brakes were applied.

Four points a, b, c and d lie on a straight level road. A car, travelling with uniform retardation, passes point a with a speed of 30 m's and passes point b with a speed of 20 m/s.

The distance from a to b is 100 m. The car comes to rest at d.

. Find

(a) the uniform retardation of the car

-» v² = u² + 2as

202 30² + 2(a)(100)

-500 = 200 a

a = -2.5 m s²

____________________________________________

(b)the time taken to travel from a to b

-» v = u + at

20 = 30 -2.5 t

T= 4s

_____________________________________________

(c) the distance from b to d

-» v² = u² + 2as

0² 202 + 2(-2.5)(s)

s = 80 m

_____________________________________________

(d)the speed of the car at c, where e is the midpoint of [bd].

-» v² = u² + 2as

= 20² + 2(-2.5)(40)

= 200

• v= 10√ or 14.1 m s-¹

hope it was helpful to you