Question

19. A train starting from rest attains a velocity of 7 km/h in 5 min. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance travelled by the train for attaining this velocity.​

Answer 1

Answer:

Appropriate Question :-

• A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance travelled by the train for attaining this velocity.

Given :-

• A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform.

To Find :-

• What is the acceleration of the train.
• What is the distance travelled by the train for attaining this velocity.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

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

$\clubsuit$ Third Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v^2 =\: u^2 + 2as}}}$

where,

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

Solution :-

First, we have to convert the final velocity km/h into m/s :

$\implies \sf Final\: Velocity =\: 72\: km/h$

$\implies \sf Final\: Velocity =\: 72 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Final\: Velocity =\: \dfrac{360}{18}\: m/s$

$\implies \sf\bold{\purple{Final\: Velocity =\: 20\: m/s}}$

Again, we have to convert the time taken minutes into seconds :

$\implies \sf Time =\: 5\: minutes$

$\implies \sf Time =\: 5 \times 60\: seconds\: \: \bigg\lgroup \sf\bold{\pink{1\: minutes =\: 60\: seconds}}\bigg\rgroup$

$\implies \sf\bold{\purple{Time =\: 300\: seconds}}$

Now, we have to find acceleration :

Given :

• Initial Velocity = 0 m/s
• Final Velocity = 20 m/s
• Time Taken = 300 seconds

According to the question by using the formula we get,

$\implies \sf 20 =\: 0 + a(300)$

$\implies \sf 20 - 0 =\: 300a$

$\implies \sf 20 =\: 300a$

$\implies \sf \dfrac{2\cancel{0}}{30\cancel{0}} =\: a$

$\implies \sf \dfrac{2}{30} =\: a$

$\implies \sf 0.067 =\: a$

$\implies \sf\bold{\red{a =\: 0.067\: m/s^2}}$

${\small{\bold{\underline{\therefore\: The\: acceleration\: of\: the\: train\: is\: 0.067\: m/s^2\: .}}}}$

Now, we have to find the distance travelled :

Given :

• Final Velocity = 20 m/s
• Initial Velocity = 0 m/s
• Acceleration = 0.067 m/s²

According to the question by using the formula we get,

$\implies \sf (20)^2 =\: (0)^2 + 2 \times 0.067 \times s$

$\implies \sf 400 =\: 0 + 0.134 \times s$

$\implies \sf 400 - 0 =\: 0.134s$

$\implies \sf 400 =\: 0.134s$

$\implies \sf \dfrac{400}{0.134} =\: s$

$\implies \sf 2985.07 =\: s$

$\implies \sf s \approx 3000\: m$

$\implies \sf\bold{\red{s =\: 3000\: m}}$

${\small{\bold{\underline{\therefore\: The\: distance\: travelled\: by\: the\: train\: for\: attaining\: this\: velocity\: is\: 3000\: m\: .}}}}$