Question

a body starts from rest and is uniformly accelerated for 30 seconds the distance travelled in the first 10 second is X1 the next 10 second is X2 and the last 10 second is x 3 then find X1 : x2 : x3

Answer 1

Initial velocity, u = 0
Acceleration = a
Distance travelled in the 1st 10s is, X1
0 + (1/2)a(10^2) = 50a

Distance travelled in the next 10 s is, X2 = [0 + (1/2)a(20^2)] – S
X1 = 200a – 50a = 150a

Distance travelled in the last 10 s is, X3 = [0 + (1/2)a(30^2)] – (X1 + X2) = 450a – 50a – 150a = 250a

Required ratio is, X1 : X2 : X3 = 50 : 150 : 250 = 1 : 3 : 5

Answer 2

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.