Question

get it? identify what is the shape of a position - time graph of an object traveling with constant acceleration? get it? identify what is the shape of a velocity - time graph of an object traveling with constant acceleration?

Explanation:

Step1: Recall kinematic equations

The position - time relation for an object with constant acceleration $a$ starting with initial velocity $v_0$ and initial position $x_0$ is $x = x_0+v_0t+\frac{1}{2}at^{2}$. This is a quadratic function of time $t$.

Step2: Determine shape of position - time graph

A quadratic function $y = Ax^{2}+Bx + C$ (in our case $x$ is a function of $t$) has a parabolic shape. So, the position - time graph of an object with constant acceleration is a parabola.

Step3: Recall velocity - time relation

The velocity - time relation for an object with constant acceleration $a$ starting with initial velocity $v_0$ is $v=v_0 + at$. This is a linear function of time $t$, where the slope is the acceleration $a$ and the $y$-intercept is $v_0$.

Step4: Determine shape of velocity - time graph

A linear function $y=mx + b$ (in our case $v$ is a function of $t$, $m = a$ and $b = v_0$) has a straight - line shape. So, the velocity - time graph of an object with constant acceleration is a straight line.

Answer:

The shape of a position - time graph of an object traveling with constant acceleration is a parabola.
The shape of a velocity - time graph of an object traveling with constant acceleration is a straight line.