Calculate the average velocity for a remote controlled vehicle that starts with a velocity of 1.0 m/s [forward] and then accelerates at 0.08 m/s2 [backward] for 4.0 s.

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"Accelerates backward" probably means "decelerates". In other words, the acceleration is `- 0.08 m / s^2` while the initial velocity is `1.0 m / s .` This way the velocity at a time t seconds is `v = v( t ) = 1.0 - 0.08 t .`

The average...

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Hello!

"Accelerates backward" probably means "decelerates". In other words, the acceleration is `- 0.08 m / s^2` while the initial velocity is `1.0 m / s .` This way the velocity at a time t seconds is `v = v( t ) = 1.0 - 0.08 t .`

The average value of this velocity from `t = 0` seconds to `t = 4` seconds is

`1 / 4 int_0^4 (1.0 - 0.08 t) dt = 1 / 4 (t - 0.04 t^2 )_(t=0)^4 = `

`=1 - 0.01 * 16 = 1 - 0.16 = 0.84 (m / s) . `

So, although the velocity of the remote controlled vehicle decreases, it remains positive and its average is also positive, namely `0.84 m /s .`

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