Question

a particle starting with certain initial velocity and uniform acceleration covers a distance of 12m in first 3 sec and distance of 30m in next 3 sec. find the initial velocity of the particle

Answer 1

Hey

Please refer to the attachment

Answer 2

1 ms^-1

Given:

Distance covered by the particle in first 3 sec = 12 meters

Distance covered by the particle in the next 3 sec = 30 meters

To Find:

Initial Velocity of the particle

Calculating:

Calculating the initial velocity of the particle when time is 3 seconds and distance 12 meters:

We use the formula:

S = ut + 1/2 a t^2

Now substituting the values known to us in this formula we get:

12 = u x 3 + 1 / 2 x a x 9

Multiplying the whole equation by 2:

24 = 6u + 18a

Now dividing the whole equation by 3 to simplify:

8 = 2u + 3a --------------Equation 1

Calculating the initial velocity of the particle when time is 6 seconds and distance 30 meters:

42 = u x 6 + 1/2 x a x 36

42 = 6u + 18a

Dividing this equation by 6 for simplifying:

7 = u + 3a -----------------Equation 2

Subtracting equation 2 from equation 1:

8 - 7 = 2u - u + 3u - 3u

1 = u - 0

u = 1 ms^-1

Therefore the initial velocity of the particle is 1 ms^-1.