Question

a particles moving with a uniform acceleration travels 24m and 64m i the first two consecutive intervals of 4 sec each .its initial velocity is

Answer 1

After that

4u=64-24a
u=64-24a/4
u=16-6a answer

I hoped this is sufficient

Answer 2

Answer:

The initial velocity is 7 m/s.

Explanation:

The particle movement is given with uniform acceleration with two consecutive interval of time, the initial velocity is calculated using equation of motion, as follows –

To find: Initial velocity, u

Time$t_{1}$= 4 sec and $t_{2}$ = 4 + 4 = 8 sec

Acceleration = a

Displacement $s_{1}$= 24 m and $s_{2}$ = 64 + 24 = 88 m  

Using second equation of motion, we get –

$\begin{array}{l}\bold{{s=u \times t+\frac{1}{2} a t^{2}}} \\ {s_{1}=u \times t_{1}+\frac{1}{2} a t_{1}^{2}} \\ {24=u \times 4+\frac{1}{2} a(4)^{2}} \\ {24=4 u+\frac{1}{2} a \times 16}\end{array}$

24 – 8a = 4u  

6 – 2a = u ______( 1)

$\bold{s_{2}=u \times t_{2}+\frac{1}{2} a t_{2}^{2}}$

$\begin{array}{l}{88=u \times 8+\frac{1}{2} a(8)^{2}} \\ {88=8 u+\frac{1}{2} a \times 64}\end{array}$

88 – 32 a = 8u

22 – 8 a = 2 u

11 – 4 a = u _______(2)

Equating both equation together we have,

6 – 2a = 11 – 4a

4 a – 2a = 11 -6

2 a=5=$\frac{5}{2}$

Substitute the value of a in equation 1

12 – 2a = u

12-2$\times \frac{5}{2}=u$

12 – 5 =u

u = 7 m/s