Each of the three graphs represents accelerat | vedclass

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(D) Speed increases when the velocity and acceleration have the same sign. Given that the object has a positive velocity at $t_1$,its speed will incre

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graphs $I, II$ and $III$

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(D) Speed increases when the velocity and acceleration have the same sign. Given that the object has a positive velocity at $t_1$,its speed will increase if the acceleration remains positive throughout the interval from $t_1$ to $t_2$. In graph $I$,the acceleration $a$ is positive and increasing,so the velocity continues to increase,and the speed increases. In graph $II$,the acceleration $a$ is constant and positive,so the velocity increases linearly,and the speed increases. In graph $III$,the acceleration $a$ is positive throughout the interval $[t_1, t_2]$,although it is decreasing. Since $a > 0$,the velocity continues to increase,and therefore the speed increases. Thus,in all three graphs,the acceleration is positive,which means the velocity increases,and consequently,the speed increases for the entire interval.

Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time $t_1$. Which graphs show an object whose speed is increasing for the entire time interval between $t_1$ and $t_2$?

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