Question

Position of a particle as a function of time is given as $x=5t^2+4t+3$. Find the velocity and acceleration of the particle at $t=2s$?

• A. $24m/s,10m/s^2$
• B. $24m/s,100m/s^2$
• C. $14m/s,10m/s^2$
• D. $24m/s,20m/s^2$

Answer 1

The correct option is A $24m/s,10m/s^2$

The displacement is given as $x=5t^2+4t+3$

$\Rightarrow x-3=5t^2+4t$

assuming $x-3=s$,

$s=4t+\frac{1}{2}10t^2$

comparing this with $s=ut+\frac{1}{2}a{t}^2$

we get $u=4m/s$ and $a=10m/s^2$

so velocity at $t=2sec$ is $v=u+at=4+10\times 2=24m/s$