a graph shows distance on the vertical axis and the time on the horizontal axis. If the speed is steady increa?

Question

a graph shows distance on the vertical axis and the time on the horizontal axis. If the speed is steady increasing, what will the line representing speed look like on the graph?

a. it will be a straight diagonal
b. it will be a straight line that has a very steep slope
c. it will be an irregular line with no pattern to it
d. it will be a curved line

Answer 1

If the velocity is increasing with time, then the object is accelerating and the displacement/ time graph will be curved. answer is d

Answer 2

If the speed were constant, then the distance would increase by a constant amount per unit of time. This would give a straight line (with a slope corresponding to the speed). If the speed increases steadily, then for each unit of time, the new distance (added to the old distance) would be a bit more. The graph would show a line that climbed faster and faster with time: a curved line, with the slope increasing steadily. The slope still shows the speed (increasing steadily). The rate of increase of the slope (meaning: the slope of the slope) is called the acceleration. If you want to get technical about it: the graph would be a portion of a parabola. If the graph could be represented by a function of time f(t), then f(t) would be the distance traveled at time t. The first differential (the slope fo f(t)), often written f'(t), is the speed. The second differential f"(t) is the acceleration. It really becomes easy once you've done a few.

Answer 3

On a distance time graph, speed is the gradient of the line. Since the speed is steadily increasing, the answer is d.