Question

The acceleration of the particle is

• A. 0
• B. 4 m/s²
• C. -4 m/s²
• D. None of these

Answer 1

Answer: (C)

-4 m/s²

Answer 2

The position of the particle is given by $x(t) = 2(t - t^2) = 2t - 2t^2$.

The velocity of the particle is the first derivative of position with respect to time: $v(t) = \frac{dx}{dt} = \frac{d}{dt}(2t - 2t^2) = 2 - 4t$.

The acceleration of the particle is the first derivative of velocity with respect to time (or the second derivative of position): $a(t) = \frac{dv}{dt} = \frac{d}{dt}(2 - 4t) = -4$.

The acceleration is constant and equal to $-4$ m/s².