What is the average speed of an object that is moving at $25 \frac{m}{s}$ $25 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 2 - 2 t^{2}$ $a(t) =2-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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What is the average speed of an object that is moving at $25 \frac{m}{s}$ $25 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 2 - 2 t^{2}$ $a(t) =2-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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Answer 1 · 2017-06-11T00:03:50

$1 \frac{m}{s}$ $1 m/s$

Explanation:

NOTE: I am using the given a(t) as the acceleration term. Dimensionally, that doesn’t look quite right $(\frac{m}{s^{2}})$ $(m/(s^2))$ ?? If it should be $a = 2 – 2*t^2$ then the calculation of the final velocity will be different.

Average Velocity
$v_a = (v_f + v_i) / 2$
where
$v_a$ = average velocity (m/s)
$v_i$ = initial velocity (m/s)
$v_f$ = final velocity (m/s)

Final Velocity
$v_f = v_i + a*t$
where
$a$ = acceleration $(m/(s^2))$
t = time taken (s)

In this case:
$v_f = v_i + (2 – 2*t^2)$ ; $v_f = 25 + (2 – 2*5^2)$
$v_f = 25 + -48 = -23$
It is moving backwards, as indicated by the negative acceleration relative to the starting point. It initially had a forward direction, so it changed direction as well as velocity.

The average velocity is thus:

$v_a = (v_f + v_i) / 2 = (-23+ 25)/2 = 1 m/s$

This positive value just means that at time (5) it has not yet quite reached the location it was at at time (0). On average it only moved 1 meter over the time span and is now heading back.

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What is the average speed of an object that is moving at $25 \frac{m}{s}$ $25 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 2 - 2 t^{2}$ $a(t) =2-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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What is the average speed of an object that is moving at 25 m/s25ms25 m/s at t=0t=0t=0 and accelerates at a rate of a(t) =2-2t^2a(t)=2−2t2a(t) =2-2t^2 on t in [0,5]t∈[0,5]t in [0,5]?

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Explanation:

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What is the average speed of an object that is moving at $25 \frac{m}{s}$ $25 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 2 - 2 t^{2}$ $a(t) =2-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?