Question

A train has a total mass of 7.5 × $10^{5}$ kg.

(a) The train accelerates from rest at a constant rate along a straight, horizontal track.

It reaches a speed of 24 m / s in 60 s.

Calculate

(i) the train’s acceleration,

acceleration = ..................................................

(ii) the resultant force acting on the train.

force = ..................................................

Answer 1

Given

• Mass = 7.5 × 10⁵ kg
• Initial Velocity = 0 m/s
• Final Velocity = 24 m/s
• Time = 60 sec

To Find

• Acceleration of the train
• Force applied on the train

Solution

● v = u + at [First Equation of Motion]

● F = ma

✭ Acceleration of the train :

→ v = u + at

→ 24 = 0 + a × 60

→ 24 = 0 + 60a

→ 24/60 = a

→ Acceleration = 0.4 m/s²

━━━━━━━━━━━━━━━━━━━━━━━━━

✭ Force Applied on the train :

→ F = ma

→ F = 7.5 × 10⁵ × 0.4

→ F = 3 × 10⁵ N

Answer 2

Answer:

Given :-

• A train has a total mass of 7.5 × 10⁵ kg.
• The train accelerates from rest at a constant rate along a straight, horizontal track and its reaches a speed of 24 m/s in 60 seconds.

To Find :-

• What is the acceleration of a train.
• What is the resultant force acting on the train.

Formula Used :-

❶ To find acceleration of a train,

By using the first equation of motion we know that,

$\sf\boxed{\bold{\large{v\: =\: u\: +\: at}}}$

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

❷ To find resultant force acting on the train,

$\sf\boxed{\bold{\large{F\: =\: ma}}}$

where,

• F = Force
• m = Mass
• a = Acceleration

Solution :-

❶ To find the acceleration of the train,

Given :

• Final velocity = 24 m/s
• Initial velocity = 0 m/s
• Time = 60 seconds

According to the question by using the formula we get,

⇒ 24 = 0 + a(60)

⇒ 24 = 0 + 60a

⇒ 24 = 60a

⇒ $\dfrac{24}{60}$ = a

⇒ 0.4 = a

➠ a = 0.4 m/s²

$\therefore$ The acceleration of a train is 0.4 m/s² .

❷ To find resultant force acting on a train,

We get,

• Mass = 7.5 × 10⁵ kg
• Acceleration = 0.4 m/s²

According to the question by using the formula we get,

↦ F = (7.5 × 10⁵) × 0.4

↦ F = 7.5 × 0.4 × 10⁵

➥ F = 3 × 10⁵ N

$\therefore$ The resultant force acting on a train is 3 × 10⁵ .