Question

A particle moves along x-axis as $x=4(t-2)+a(t-2{)}^2$ Which of the following is true?

• A. The initial velocity of particle is 4
• B. The acceleration of particle is 2a
• C. The particle is at origin at t = 0
• D. None of these

Answer 1

The correct option is B The acceleration of particle is 2a

$x=4(t-2)+a(t-2{)}^2$

At $t=0,x=-8+4a=4a-8$

$v=\frac{dx}{dt}=4+2a(t-2)$

At $t=0,v=4-4a=4(1-a)$

But acceleration, $a=\frac{d^{2}x}{d{t}^2}=2a$