Problem

Graphs of the velocity functions of two particles are shown, where $t$ is measured in seconds. (a) When is the particle in figure (a) speeding up? (Enter your answer using interval notation.) When is the particle in figure (a) slowing down? (Enter your answer using interval notation.) (b) When is the particle in figure (b) speeding up? (Enter your answer using interval notation.) When is the particle in figure (b) slowing down? (Enter your answer using interval notation.)

Solution

Step 1 :Given the velocity function of a particle, we need to find when the particle is speeding up or slowing down. A particle is speeding up when its velocity and acceleration have the same sign, and it is slowing down when its velocity and acceleration have opposite signs.

Step 2 :To find the intervals where the particle is speeding up or slowing down, we need to find the acceleration function, which is the derivative of the velocity function.

Step 3 :Then, we find the intervals where the velocity and acceleration functions have the same sign (for speeding up) or opposite signs (for slowing down).

Step 4 :Without specific functions or graphs, it is impossible to provide a specific answer.

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Source: https://solvelyapp.com/problems/7488/

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