On an acceleration-time graph, which quantity does the area between the graph and the time axis give?
A truck rolls onto an empty highway on-ramp and holds a steady acceleration of 3 m/s² for 4 s. How much velocity does the truck pick up? You've already seen that the area between an acceleration-time graph and the time axis is the change in velocity. So one multiplication answers the question.
Read the rectangle off the graph. Its height is the acceleration, 3 m/s². Its width is the time it lasts, 4 s.
Multiply height by width:
area = 3 × 4 = 12
Δv = 12 m/s, because the area between an acceleration-time graph and the time axis is the change in velocity.
The graph shows a speedboat's acceleration-time graph. Calculate the boat's change in velocity over the stretch shown.
Read the rectangle off the graph:
height = 5 m/s²
width = 3 s
The area is height × width:
area = 5 × 3 = 15
Δv = 15 m/s
The figure shows a car's acceleration-time graph as it joins a highway. Calculate the car's change in velocity over the full stretch shown, in m/s.
Careful with the width. If the truck's rectangle ran from 1 s to 5 s instead, it would still be 4 s wide. The width is the stretch of time, not the clock reading where the stretch ends.
The figure shows a fishing boat's acceleration-time graph. The acceleration starts partway through the stretch shown. Calculate the boat's change in velocity, in m/s.
Some graphs hold one acceleration and then another: the truck surging, then easing off. Each rectangle gives the velocity change for its own stretch. Add the areas for the total change.
The graph shows a freight train's acceleration-time graph with two rectangles. Calculate the train's total change in velocity.
Read the first rectangle off the graph:
area = 2 × 3 = 6
Read the second rectangle off the graph:
area = 4 × 2 = 8
Add the two velocity changes:
Δv = 6 + 8
Δv = 14 m/s
The figure shows a metro train's acceleration-time graph with two rectangles. Calculate the train's total change in velocity over the full stretch shown, in m/s.
The figure shows a minivan's acceleration-time graph. Calculate the minivan's change in velocity, in m/s.
The figure shows an electric motorcycle's acceleration-time graph with two rectangles. Calculate the motorcycle's total change in velocity over the full stretch shown, in m/s.