Question

from a stopped position, a car starts to accelerate at 3 m/sec². which graph below best represents the motion of the car?

Explanation:

Step1: Recall motion - equation for uniformly - accelerated motion

The equation for the displacement $d$ of an object starting from rest ($u = 0$) under constant acceleration $a$ is $d=ut+\frac{1}{2}at^{2}$. Since $u = 0$, the equation simplifies to $d=\frac{1}{2}at^{2}$. Here, $a = 3\ m/s^{2}$, so $d=\frac{3}{2}t^{2}$.

Step2: Analyze the nature of the displacement - time graph

The function $d=\frac{3}{2}t^{2}$ is a quadratic function of the form $y = Ax^{2}$ (where $y = d$, $x = t$, and $A=\frac{3}{2}$). The graph of a quadratic function $y = Ax^{2}$ is a parabola opening upwards.

Answer:

B. W