The graph of the scalar component of the position versus time for a particle mov

Question

The graph of the scalar component of the position versus time for a particle moving horizontally is a parabola (figure). What can be said about the particle's acceleration? The acceleration is increasing and in the positive x direction. The scalar component of the horizontal position can be written as x(t) = ct^2 + dt + e. The acceleration is the second derivative of this function a(t) = c, where c will be a positive number given the shape of the curve. The acceleration is constant and in the negative x direction. The scalar component of the horizontal position can be written as x(t) = dt + e. The acceleration is the second derivative of this function a(t) = d, where d will be a negative number given the shape of the curve. The acceleration is increasing and in the negative x direction. The scalar component of the horizontal position can be written as x(t) = dt + e. The acceleration is the second derivative of this function a(t) = d, where d will be a negative number given the shape of the curve. The acceleration is constant and in the positive x direction. The scalar component of the horizontal position can be written as x(t) = ct^2 + dt + e. The acceleration is the second derivative of this function a(t) = 2c, where c will be a positive number given the shape of the curve.

Explanation / Answer

Option d is correct.

Since it is upward opening parabola, acceleration will be positive and constant and will be given by second derivative of the quadratic equation.

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