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7. MOTION
hard
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.
A
$\left(u+5 a\right)\, m$
B
$\left(u+\frac{3}{2} a\right)\, m$
C
$\left(u+\frac{9}{2} a\right)\, m$
D
$\left(u+4a\right)\, m$
Solution
Using the equation of motion $s=u t+\frac{1}{2} a t^{2}$
Distance travelled in $5\, s$ $s=u \times 5+\frac{1}{2} a \times 5^{2}$
Or $ s=5 u+\frac{25}{2} a$ ……….. $(i)$
Similarly, distance travelled in $4 \,s$ , $s^{\prime}=4 u+\frac{16}{2} a$ ………… $(i i)$
Distance travelled in the interval between $4^{\text {th }}$ and $5^{\text {th }}$ second $=\left(s-s^{\prime}\right)=\left(u+\frac{9}{2} a\right)\, m$
Standard 9
Science
