Question

Which of the following graphs best represents the motion of an object with increasing speed?

Option 1: A graph with distance increasing linearly with time.
Option 2: A graph with distance increasing quadratically with time.
Option 3: A graph with distance increasing exponentially with time.
Option 4: A graph with distance increasing at a constant rate with time.

Answer 1

The graph that best depicts an object with increasing speed is the one with the distance increasing quadratically with time, as this indicates accelerating motion and thus an increasing velocity.

Step-by-step explanation:

The graph that best represents the motion of an object with increasing speed is Option 2: A graph with distance increasing quadratically with time. This is because as an object speeds up, the distance it covers in the same interval of time keeps getting larger. When we look at a Distance vs. Time graph, constant velocity is indicated by a straight line at a constant slope. Meanwhile, increasing velocity results in a curve where the slope (representing speed) becomes steeper as time progresses. Therefore, a quadratic increase in distance over time suggests that not only is the object moving, but it is also accelerating, thereby steadily increasing its velocity.