Question

A body starts from rest is uniformly accelerated for 15 s. The distance travelled in first 5 s is x₁, next 5 s is x₂ and the last 5 s is x3. Then​

Answer 1

Answer:

1 : 3 : 5

In this question we use the formula:

S = 1/2 a x t^2

Distance traveled by the body in first 10 sec (x1):

S = 1/2 a x t^2

Substituting the values known to us from the question in this equation we get:

=> x1 = 1/2 x a x 10^2

=> x1 = 100 x a x 1/2

=> x1 = 50 a

Distance traveled by the body in the next 10 sec (x2):

S = 1/2 a x t^2 - 1/2 x a x 10^2

Substituting the values known to us from the question in this equation we get:

=> x2 = 1/2 x a x 20^2 - 1/2 x a x 10^2

=> x2 = 200 a - 50 a

=> x2 = 150 a

Calculating the distances traveled in the last 10 sec (x3):

S = 1/2 a x t^2 - 1/2 x a x 10^2 - 1/2 x 20^2

Substituting the values known to us from the question in this equation we get:

=> x3 = 1/2 a x 30^2 - 1/2 x a x 10^2 - 1/2 x 20^2

Solving we get:

=> x3 = 1/2 x a x 500

=> x3 = 250 a

Now calculating x1:x2:x3

= 50 a : 150 a : 250 a

In simplest ratio we get:

= 1 : 3 : 5

Therefore, the ratio of x1:x2:x3 is 1 : 3 : 5.

Answer 2

Answer:

The ratios of x1 : x2 : x3 = 1 : 3 : 5

Explanation:

Given :

Initial Velocity (u) = 0 m/s

Thr body is accelerated for 15 seconds.

This acceleration is divided into three parts, 5 seconds each.

Let time (t) = 5 seconds.

To be Calculated -

x1 : x2 : x3

Formula to be Used :

$s \: = ut \: + \frac{1}{2} \times a {t}^{2}$

where s is the distance covered by the body, u is initial velocity, t is time taken and a is acceleration.

Calculations :

For the first 5 seconds,

u = 0 m/s

$x1 = \frac{1}{2} \times a {t}^{2}$

For the next 5 seconds,

$x1 + x2 = \frac{1}{2} \times a {(2t)}^{2} = 4x1$

$x2 = 3x1$

For the last 5 seconds,

$x1 + x2 + x3 = \frac{1}{2} \times a {(3t)}^{2} = 9x1$

$x3 = 9x1 - x1 - 3x1 = 5x1$

Now, The ratios of x1 : x2 : x3 = 1 : 3 : 5 .

Concept :

There are three equations of motion :

$v \: = u \: + at \: \\ s \: = ut \: + \frac{1}{2} a {t}^{2} \\ {v}^{2} - {u}^{2} = 2as$

These equations are used when acceleration is constant for solving any problem.

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