Question

The graph represents velocity over time... What is the acceleration? a) -0.4 m/s² b) -0.2 m/s² c) 0.2 m/s² d) 0.4 m/s²

Answer 1

Acceleration can be determined from the slope of a velocity-time graph. For a straight line where velocity changes from 0 to 20 m/s over 10 seconds, the acceleration is 2 m/s². A negative slope represents negative acceleration or deceleration.

Step-by-step explanation:

The student's question pertains to the concept of acceleration in a velocity versus time graph. To determine acceleration from such a graph, one needs to understand the slope of the line. For a graph where velocity increases from 0 m/s to 20 m/s in 10 seconds, the average acceleration (a) can be calculated using the formula a = ∆v / ∆t, where ∆v is the change in velocity and ∆t is the change in time. Therefore, a = (20 m/s - 0 m/s) / (10 s - 0 s), which is 2 m/s². This indicates constant acceleration, as suggested by a straight line with a constant slope on the velocity-time graph.

In cases where the acceleration has a negative value, the velocity is decreasing over time, indicating negative acceleration or deceleration. If a velocity-time graph shows a slope going from a positive value to zero, the slope of the graph indicates a negative acceleration value equal to the slope of the line.

Answer 2

The acceleration of the graph is 0.2 m/s². Option C

What is the acceleration?

In a uniformly accelerated motion, the velocity at time t is given by:

v = at

where

a = the acceleration

t = the time.

Given the previous equation, if v is plotted versus t, we find a straight line

The slope of the line represents acceleration, a

Looking at the graph, when the time goes from 10 s to 20 s, the velocity increases from 4 m/s to 6 m/s.

So

The slope of the line = change in velocity / change in time

= (6 m/s - 4 m/s) / (20 s - 10 s)

= 2 m/s / 10 s

= 0.2 m/s²

Hence, 0.2 m/s² is the acceleration