26. (a)To graph the velocity, we estimate the slopes at severalpoints as follows, then connect the points to create asmooth curve.To graph the acceleration, we estimate the slope of thevelocity graph at several points as follows, and thenconnect the points to create a smooth curve.(b)}ddst}530t23t2[0, 15] by [2300, 100]}ddt22s}53026t[0, 15] by [2100, 50]The graphs are very similar.27. (a)Solving 1605490t2gives t5 6}47}.It took }47}of a second. The average velocity was sec = 280 cm/sec.(b)v5s9(t)5980ta5s0(t)5980The velocity was s91}47}25560 cm/sec.The acceleration was s01}47}25980 cm/sec2.(c)Since there were about 16 flashes during }47}of a second,the light was flashing at a rate of about 28 flashes persecond.28.Graph C is position, graph A is velocity, and graph B isacceleration.A is the derivative of C because it is positive, negative, andzero where C is increasing, decreasing, and has horizontaltangents, respectively. The relationship between B and A issimilar.
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Velocity, dy, 160 cm, 980 cm, 280 cm, 560 cm