Question

Obtain a relation for the displacement of an object moving with a uniform acceleration in the interval between $4^{th}$ and $5^{th}$ seconds. Assume zero initial velocity.

• A. $\frac{9}{2}\times$acceleration
• B. $\frac{2}{9}\times$acceleration
• C. $\frac{7}{2}\times$acceleration
• D. $\frac{5}{2}\times$acceleration

Answer 1

The correct option is A $\frac{9}{2}\times$acceleration

From second equation of motion, $s=ut+\frac{1}{2}a{t}^2$
The displacement after t = 5 seconds will be $s_5=5u+\frac{1}{2}a{5}^2$
The displacement after t = 4 seconds will be $s_4=4u+\frac{1}{2}a{4}^2$
Displacement between 4th and 5th second will be $s_5-s_4=(5u+\frac{1}{2}a{5}^2)-(4u+\frac{1}{2}a{4}^2)$.
$=u+\frac{1}{2}a(25-16)=u+\frac{9}{2}a$
$=\frac{9}{2}a$