In physics, when is an object accelerating?
A city bus leaves its stop, gaining speed briskly for 4 s: an acceleration of 3 m/s². Then the driver eases off and cruises for 3 s at zero acceleration. For the last 3 s of the stretch the driver brakes gently: an acceleration of −2 m/s². Three stretches, three accelerations, and one picture that holds all three.
This picture is the bus's acceleration-time graph. It plots acceleration, in m/s², up the vertical axis against time, in s, along the horizontal axis. You've already read position-time graphs and velocity-time graphs. The last graph of the family reads the same way.
Try it on the bus at t = 2 s. The line stands at 3 m/s² there: the speeding-up stretch.
The graph shows a cargo van's acceleration. What is the van's acceleration at t = 2 s? Enter the value in m/s², sign included.
A step below the time axis is a negative acceleration. The bus's braking step sits at −2 m/s².
The graph shows a car's acceleration. What is the car's acceleration at t = 4 s? Enter the value in m/s², sign included.
A line ON the time axis is a real reading too, not a gap. The axis marks zero acceleration. From t = 4 s to t = 7 s the bus's acceleration is 0 m/s², so its velocity is not changing there.
One more feature. An acceleration can change abruptly: the driver steps off the pedal in an instant. So the line can jump straight from one level to the next, and acceleration-time graphs often look like flat steps, like the bus's three.
The graph shows a tow truck's acceleration. What is the truck's acceleration at t = 6 s?
Find t = 6 s on the time axis.
Go straight up to the line: at t = 6 s the truck is on its second step.
Read across to the acceleration axis: 5 m/s².
The truck's acceleration at t = 6 s is a = 5 m/s².
The graph shows a boat's acceleration. What is the boat's acceleration at t = 7 s?
Find t = 7 s on the time axis.
The line lies on the time axis there.
A line on the axis is a real reading: zero acceleration.
The boat's acceleration at t = 7 s is a = 0 m/s². The boat's velocity is not changing at that moment.
The graph shows a shuttle's acceleration in three stages. What is the shuttle's acceleration at t = 5 s? Enter the value in m/s², sign included.
The graph shows a courier bike's acceleration in three steps. What is the bike's acceleration at t = 3 s?
The graph shows a tour bus's acceleration. What is the bus's acceleration at t = 5 s?
The graph shows a metro car's acceleration in four steps. What is the car's acceleration at t = 9 s?