Question

A particle moves on a line according to the law $s=a{t}^2+bt+c$ . If the displacement after $1$ sec is $16$cm, the velocity after $2$ sec is $24$ cm/sec and acceleration is $8cm/se{c}^2$, then

• A. $a=4,b=8,c=4$
• B. $a=4,b=4,c=8$
• C. $a=8,b=4,c=4$
• D. none of these

Answer 1

The correct option is A $a=4,b=8,c=4$

$s=a{t}^2+bt+c$

$s\left(1\right)=a+b+c$

$\Rightarrow a+b+c=16$ .....(i)

Velocity$v=\frac{ds}{dt}=2at+b$

$v\left(2\right)=4a+b$

$\Rightarrow 4a+b=24$ ......(ii)

Acceleration$\frac{dv}{dt}=2a$

$\Rightarrow 2a=8$

$\Rightarrow a=4$

substitute in velocity equation

$4\left(4\right)+b=24\Rightarrow b=24-16=8$

$\Rightarrow b=8,a=4$

substitute in displacement equation

$4+8+c=16\Rightarrow c=16-12=4$

$\therefore a=4,b=8,c=4$