Question

A body moving along a straight line with a uniform acceleration covers $20 \,cm$ in one second and $30\, cm$ in very next second. The body has an acceleration of

• A. $10 \, cm$ $s^{-2}$
• B. $5\, cm$ $s^{-2}$
• C. $30\, cm$ $s^{-2}$
• D. $20 \, cm$ $s^{-2}$

Answer 1

Answer: (A)

Let the initial velocity be u and acceleration be a.
Case 1:
Distance covered $S =20 m$
Time taken $t =1 s$
Using $S=u t+\frac{1}{2} a t^{2}$
Or $\quad 20=u(1)+\frac{1}{2} a(1)^{2}$
$\Longrightarrow 20= u +\frac{ a }{2}$
We get $u =20-\frac{ a }{2}$
Case 2 :
Total distance covered $S =20+30=50 m$
Total time taken $t =1+1=2 s$
So, $50=u(2)+\frac{1}{2} a(2)^{2}$
or $50=2 u +2 a$
Or $50=2\left(20-\frac{a}{2}\right)+2 a$
Or $50=40-a+2 a$
$\Longrightarrow a =10 m / s ^{2}$