Question

A train accelerates uniformly from 36 km/h to 72 km/h in 20 s.Find the distance travelled by it.

Answer 1

Answer:

The distance traveled by car is 300m.

Explanation:

First, we will need to find the acceleration of the train from the first equation of motion which is given as;

$v=u+at$    (1)

Where,

v=final velocity

u=initial velocity

a=acceleration of the body

t=time during which the motion occurs

From the question we have,

The initial velocity(u)=36km/hr=$36\times \frac{5}{18}$=10m/s

The final velocity(v)=72km/hr=$72\times \frac{5}{18}$=20m/s

The time during which this change in velocity takes place(t)=20s

By inserting values in equation (1) we get;

$20=10+a\times 20$

$a=\frac{20-10}{20}$

$a=\frac{1}{2} \ m/s^2$     (2)

We will get the distance traveled(S) by train will be calculated through the second equation of motion. Which is given as,

$S=ut+\frac{1}{2}at^2$   (3)

By placing the values in equation (3) we get;

$S=10\times 20+\frac{1}{2}\times \frac{1}{2} \times (20)^2$

$S=200+100$

$S=300\ m$

Hence, the distance traveled by car is 300m.

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Answer 2

Answer:

The distance traveled is 300m.

Explanation:

Given:

Initial velocity(u) = 36km/h = (36×1000)/3600 = 10m/s

Final velocity(v) = 72km/h = (72×1000)/3600 = 20m/s

Time(t) = 20s

To find:

Distance travelled(s) = ?

Formula:

v = u + at

s = ut + (1/2)at²

Step 1:

We first find out the acceleration using the first equation of motion. The first equation of motion is given as follows:

v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Substituting the given values, we get

20 = 10 + a(20)

20 - 10 = 20a

10 = 20a

a = 10/20

a = 1/2 m/s²

Step 2:

To find the distance traveled, we use the second equation of motion. The second equation of motion is given as follows:

s = ut + (1/2)at², where s is the distance traveled.

Substituting the given values, we get

$s = (10)(20) + (\frac{1}{2})( \frac{1}{2})(20)^2$

$s = 200 + (\frac{1}{4})(400)$

s = 200 + 100

s = 300m

Therefore, the total distance traveled by train in the 20s is 300m.

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