which of the following pairs of graphs shows the distance traveled versus time and speed versus for an object uniformly accelerated from rest?

The parabola :)

d^2x/dt^2 = a constant acceleration
dx/dt = v = initial speed Vi + a t (straight line)
x = initial x + Vi t + (1/2) a t^2
quadratic, parabola

To determine which pairs of graphs show distance traveled versus time and speed versus time for an object uniformly accelerated from rest, we need to understand the characteristics of uniformly accelerated motion.

In uniformly accelerated motion, the object's speed increases by a constant amount over equal time intervals. Since the object starts from rest, its speed at any given time can be calculated using the formula:

speed = acceleration × time

Now, let's analyze the given pairs of graphs:

Pair 1:
- Distance traveled versus time: Initially, the distance is zero, and it gradually increases with time. This graph represents a continuously increasing distance over time, which is in line with uniformly accelerated motion.
- Speed versus time: At t = 0, the speed is also zero, and then it gradually increases over time in a linear manner. This graph represents a constant acceleration, which is characteristic of uniformly accelerated motion.

Pair 2:
- Distance traveled versus time: Initially, the distance is zero, and it steadily increases with time. This graph also represents a continuously increasing distance over time, as expected in uniformly accelerated motion.
- Speed versus time: At t = 0, the speed is zero, and it increases non-linearly with time. This graph does not represent constant acceleration because the speed is not changing at a steady rate.

Pair 3:
- Distance traveled versus time: Initially, the distance is zero, and it rapidly increases with time. This graph represents a non-uniform increase in distance, which is not indicative of uniformly accelerated motion.
- Speed versus time: At t = 0, the speed is zero, and it quickly increases to a maximum value, then remains constant. This graph represents an object that accelerates to a specific speed and then maintains that speed, which is again not characteristic of uniformly accelerated motion.

Based on the analysis, only Pair 1 shows both distance traveled versus time and speed versus time graphs that represent an object uniformly accelerated from rest.