Which equation defines acceleration?
A motorcycle accelerates along a straight on-ramp. At t = 2 s it is moving at 4 m/s; at t = 5 s it is moving at 16 m/s. How hard is it accelerating? The answer is sitting in the picture of its trip.
You've already seen that the slope of a velocity-time graph is the acceleration. So the motorcycle's acceleration is one rise-over-run away.
The graph shows the motorcycle's velocity. What is the motorcycle's acceleration between t = 2 s and t = 5 s?
Read the two ends of the segment off the graph:
v = 4 m/s at t = 2 s
v = 16 m/s at t = 5 s
Find the changes, final minus initial:
Δv = 16 − 4 = 12 m/s
Δt = 5 − 2 = 3 s
Write down the equation:
a = Δv/Δt
Substitute in the values:
a = 12 / 3
Simplify:
a = 4 m/s²
The graph shows a van's velocity. Calculate the van's acceleration between t = 2 s and t = 6 s. Enter the value in m/s², sign included.
A falling segment gives a negative Δv, so the acceleration comes out negative. No extra step is needed: keep the signs, subtract final minus initial, and the arithmetic does the work.
The graph shows a tour boat's velocity. What is the boat's acceleration between t = 1 s and t = 7 s?
Read the two ends of the segment off the graph:
v = 15 m/s at t = 1 s
v = 3 m/s at t = 7 s
Find the changes, final minus initial:
Δv = 3 − 15 = −12 m/s
Δt = 7 − 1 = 6 s
Write down the equation:
a = Δv/Δt
Substitute in the values:
a = −12 / 6
Simplify:
a = −2 m/s²
The graph shows a tow truck's velocity. Calculate the truck's acceleration between t = 1 s and t = 5 s. Enter the value in m/s², sign included.
The graph shows a sled's velocity, below the time axis throughout. Calculate the sled's acceleration between t = 2 s and t = 5 s. Enter the value in m/s², sign included.
The same steps work on any straight segment of any velocity-time graph, wherever the segment sits and whichever way it leans.
The graph shows a speedboat's velocity crossing the time axis. What is the boat's acceleration between t = 1 s and t = 5 s?
The graph shows a metro train's velocity. Calculate the train's acceleration between t = 2 s and t = 8 s. Enter the value in m/s², sign included.
The graph shows a car's velocity in two stages. Calculate the car's acceleration during the second stage, from t = 3 s to 8 s. Enter the value in m/s², sign included.