Question

Given is a graph representing the position of a ball as it rolls across a table. What is the ball's average velocity? A) 80 cm/sec B) 20 cm/sec C) 200 cm/sec D) 400 cm/sec

Answer 1

Average Velocity = (size+direction of displacement)/(time for the change)

We don't know the direction in  which the ball rolled, so we can't fully describe its velocity.  The best we can do is talk about its speed.

Speed = (distance covered) / (time to cover the distance)

Distance = (ending position) - (starting position)

Distance = (80 cm) - (zero) = 80 cm

Speed = (80 cm) / (0.4 sec)

Speed = 200 m/s

Answer 2

Answer: Option C, s = 200 cm/s

Explanation:

The average velocity can be obtained by the slope of the linear function that we have in the graph, this is:

s = (y2 - y1)/(x2 - x1)

where y2 = f(x2) and y1 = f(x1)

for this we need two pairs of data, let's use the first two:

y1 = 20cm, x1 = 0.1 sec

y2 = 40cm, x2 = 0.2 sec.

then the slope is:

s = (40cm - 20cm)/(0.2s - 0.1s) = 20cm/0.1s = 200cm/s

then the correct option is C