Question

A body is moving with uniform acceleration and it covers 20m in 4th second and 30m in 8th second. Find (i) the initial velocity, (ii) the acceleration of the body.​

Answer 1

Answer:

Initial Velocity = 15 m/sec

Acceleration = 2.5 m/sec ^2

Explanation:

a = ?

d1 = 20 m

t1 = 4 sec

Velocity = Distance / Time

V1 = 5 m/sec

d2 = 30 m

t2 = 8 sec

V2 = 36/8

= 15/4 m/sec

Acceleration :

s1 = ut +1/2 at^2

20 = 0 + 1/2 a × 4^2

20= 0+ 1/2 ×a × 16

20 = 8a

a = 20/8

a = 16/4

a = 5/2

a= 2.5 m/s ^ 2

Initial Velocity :

V = u +at

5 = u - 2.5 ×4

5 = u - 10

u = 10 + 5

u = 15 m/ sec

Answer 2

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

$20 = u(4) + \frac{1}{2} a{(4)}^{2}$

$20 = 4u + \frac{4a}{2}$

$4u = 20 - \frac{4a}{2}$

$S = 20+ 30 = 50$

$t = 4 + 8 = 12$

$50 = 12(u) + \frac{1}{2} a( {12)}^{2}$

$50 = 12u + 72a$

$50 = 12(20 - \frac{4a}{2} ) + 72a$

$50 = 240a - 24a + 72a$

$50 = 240a + 48a$

$50 = 288a$

$a = \frac{288}{50}$

$a = 5.76 \: m {s}^{2}$