Question

train starting from rest attains a speed of 40 km/h. The acceleration of the train is 4 km/h^2. The time taken by the train to reach this peed is ______ hours *​

Answer 1

Given :

Initial velocity of train = zero

Final velocity of train = 40 kmph

Acceleration of train = 4 kmph²

To Find :

Time taken by the train to reach the final velocity.

Solution :

Acceleration is defined as the ratio of change in velocity to the time taken.

• It is a vector quantity having both magnitude as well as direction.
• SI unit : m/s²

Formula : $\boxed{\blue{\bf{a=\dfrac{v-u}{t}}}}$

→ v denotes final velocity

→ u denotes initial velocity

→ t denotes time

→ a denotes acceleration

By substituting the given values;

$\sf\dashrightarrow\:4=\dfrac{40-0}{t}$

$\sf\dashrightarrow\:t=\dfrac{40}{4}$

$\dashrightarrow\:\underline{\boxed{\bf{\purple{t=10\:hrs}}}}$

Answer 2

Answer:

Given :-

• The train starting from rest attains a speed of 40 km/h.
• The acceleration of the train is 4 km/h².

To Find :-

• What is the time taken by the train to reach in that speed.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

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

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

Solution :-

Given :

• Final Velocity = 40 km/h
• Initial Velocity = 0 km/h
• Acceleration = 4 km/h²

According to the question by using the formula we get,

$\dashrightarrow \bf v =\: u + at$

$\dashrightarrow \sf 40 = 0 + 4(t)$

$\dashrightarrow \sf 40 =\: 0 + 4t$

$\dashrightarrow \sf 40 - 0 =\: 4t$

$\dashrightarrow \sf 40 =\: 4t$

$\dashrightarrow \sf \dfrac{\cancel{4}0}{\cancel{4}} =\: t$

$\dashrightarrow \sf \dfrac{10}{1} =\: t$

$\dashrightarrow \sf 10 =\: t$

$\dashrightarrow \sf\bold{\red{t =\: 10\: hours}}$

$\therefore$ The time taken by the train to reach in that speed is 10 hours .

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