An object starts at rest then accelerates at a rate of 5m/s^2 for 1 second and then 2m/s^2 for 2 seconds. what is the average acceleration over time (t€[0,3]

Acceleration = (change in speed) / (time for the change)

-- during the first second, the object increases its speed to

(5 m/s²) · (1 s) = 5 m/s .

-- During the next 2 seconds, the object increases its speed by

(2 m/s²) · ( s) = 4 m/s

So at the end of the whole 3 seconds, its speed is (5 m/s) + (4 m/s) = 9 m/s

-- Over the whole time, its speed has changed from zero to 9 m/s.

Acceleration = (change in speed) / (time for the change)

Acceleration = (9 m/s) / (3 sec)

Acceleration = 3 m/s²

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