Question

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the Interval between 4^th and 5^th seconds.

Answer 1

Step 1,

Using the equation of motions we can write

$s=ut+\frac{1}{2}a{t}^2$
Distance travelled in 5 s

$s=u\times 5+\frac{1}{2}a\times 5^2$

or $s=5u+\frac{25}{2}a$ ....(i)

Similarly, distance travelled in 4s,

$s^{\prime }=4u+\frac{16}{2}a$ ....(ii)

Step 2,

Distance traveled in the interval between 4th and 5th second is

The difference between the distance traveled in 5 s and the distance traveled in 4 s

After subtracting

We get,

$(u+\frac{9}{2}a)m$

Hence the given relation is as shown above.