Question

If the law of motion in a straight line is $s=\frac{1}{2}vt$, then acceleration is

• A. Constant
• B. Proportional to t
• C. Proportional to v
• D. Proportional to s

Answer 1

The correct option is A Constant

$s=\frac{1}{2}vt\Rightarrow 2s=vt\Rightarrow 2\frac{ds}{dt}=v+t.\frac{dv}{dv}\Rightarrow 2\frac{d^{2}s}{d{t}^2}=\frac{dv}{dt}+t.\frac{d^{2}v}{d{t}^2}+\frac{dv}{dt}$
But $\frac{dv}{dt}$=acceleration (a)
$\Rightarrow 2a=a+t.\frac{da}{dt}+a\Rightarrow \frac{da}{dt}=0$ or t=0
But for whole notation t=0 is impossible so that $\frac{da}{dt}=0$ i.e., a is contant.