Question

A train starting from rest attains a velocity of 20m/s in 5min assuming that the acceleration is uniform find the distance travelled by the train for attaining the velocity?

Answer 1

Given ,

U = 0 (As, train starts from rest)

V = 20 m/s

time taken = 5 minutes

To Find :-

Total distance traveled.

Solution :-

Time taken = 5 minutes

= (5×60) seconds

= 300 seconds

From first equation of motion we have,

v = u + at.

On inserting the values in the formula

We get ,

20 = 0 + a × 300

=> a = 20/300

therefore , a = 0.066 m/s²

Now, from the 3rd eqn. of motion, we have

v² = u² + 2as

(20)² = (0)² + 2×0.066×S

=> 400 = 0.132 S

$=>\: S\: =\: {\dfrac{400}{0.132}}$

=> S = 3030.30 m

Therefore, distance traveled is 3030.30m

Short-hands Used :-

• u = Initial velocity
• v = Final velocity
• a = Acceleration
• S = Distance
• eqn = equation

Answer 2

Answer:

Given:-

intial velocity =u=0 m/s

final velocity =v=20 m/s

time taken=t=5 minutes=5×60=300seconds

To find:-

Total distance covered=s

Formula used:-

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

${:}\longrightarrow$${\boxed {s=ut+{\frac {1}{2}}at {}^{2}}}$

Now,

using first equation of motion

${:}\longrightarrow$$v=u+at$

${:}\longrightarrow$$20=0+a×300$

${:}\longrightarrow$$20=300a$

${:}\longrightarrow$$a={\frac {20}{300}}$

${:}\longrightarrow$${\underline{\boxed {\bf {a=0.066 m/s {}^{2}}}}}$

• by using second equation of motion

${:}\longrightarrow$$s=ut+{\frac {1}{2}}at {}^{2}$

${:}\longrightarrow$$s=0×300+{\frac{1}{2}}×0.066×{300}^{2}$

${:}\longrightarrow$${\underline{\boxed{\bf {s=3030.30m}}}}$