## College Physics (4th Edition)

We can rank the times, in order of the magnitude of the acceleration, from largest to smallest: $5.5~s \gt 0.5~s \gt 1.5~s = 2.5~s \gt 3.5~s = 4.5~s$
The slope of the velocity versus time graph is the acceleration. We can find the acceleration at each of the given times $t$. $t = 0.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{4.0~m/s}{1.0~s} = 4.0~m/s^2$ $t = 1.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{2.0~m/s}{2.0~s} = 1.0~m/s^2$ $t = 2.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{2.0~m/s}{2.0~s} = 1.0~m/s^2$ $t = 3.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{0~m/s}{2.0~s} = 0~m/s^2$ $t = 4.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{0~m/s}{2.0~s} = 0~m/s^2$ $t = 5.5~s$ $a = \frac{\Delta v}{\Delta t} = \frac{-5.0~m/s}{1.0~s} = -5.0~m/s^2$ We can rank the times, in order of the magnitude of the acceleration, from largest to smallest: $5.5~s \gt 0.5~s \gt 1.5~s = 2.5~s \gt 3.5~s = 4.5~s$