Question

A body moving with a constant acceleration travels 3 m and 8 m respectively in 1 s and 2 s. Calculate-

1 initial velocity and

2 the acceleration of the body

Answer 1

Step 1, Given data

The body is moving 3 m in 1 second

And 8 m in 2 seconds

Step 2, Finding the initial velocity and acceleration

From the equation of motion

We know,

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

For first condition $s=3m,t=1s$
We get

$3=u\times 1+\frac{1}{2}\times a\times 1\times 1$

$3=u+\frac{a}{2}$

$6=2u+a............\left(1\right)$

Now,
For second condition $s=8mandt=2s$
We get

$8=2u+\frac{1}{2}a\times 2^2$

$8=2u+2a$

$4=u+a............\left(2\right)$

After solving ( 1 ) and ( 2 ), we get

Initial velocity $u=2m/s$

Acceleration $a=2m/s²$