Question

post-class quiz: velocity vs time
1 multiple choice 0.5 points
on a v-t graph, the area under the curve gives the:
acceleration
position
speed
displacement

Explanation:

Velocity ($v$) is defined as the rate of change of displacement ($x$) with respect to time ($t$), so $v = \frac{dx}{dt}$. Integrating velocity over time to find displacement gives $x = \int v \, dt$, which corresponds to the area under a velocity-time (v-t) graph. Acceleration is the slope of a v-t graph, position is not directly given by the area, and speed is the magnitude of velocity with no directional component tied to this area.

Answer:

Displacement