Question

A particle moves along x-axis as $x=4(t-2)+a(t-2{)}^2$

Which of the following is true?

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

Answer 1

The correct option is A

The acceleration of particle is $2a$

Step 1: Find initial position of the particle.

Given, particle moves along x-axis,

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

At $t=0$,

Position of the particle,

$x=-8+4a=4a-8$

Step 2: Find initial velocity of the particle.

Velocity of the particle,

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

Initial velocity of the particle,

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

Step 3: Find acceleration of the particle.
acceleration, $a=\frac{dv}{dt}=2a$

Final answer: (b)