What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = \frac{t}{2} + 1$ $a(t) =t/2+1$ from $t \in [0, 2]$ $t in [0, 2]$ ?

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Answer 1 · 2016-09-29T23:44:55

I found: $v = 3 \frac{m}{s}$ $v=3m/s$

I would try integrating your acceleration to obtain the speed as:

$v (t) = \int_{0}^{2} (\frac{t}{2} + 1) d t =$ $v(t)=int_0^2(t/2+1)dt=$

$= \frac{1}{2} \frac{t^{2}}{2} + t = \frac{t^{2}}{4} + t$ $=1/2t^2/2+t=t^2/4+t$

evaluated between the two extremes:

$v_{0 \to 2} = (\frac{4}{4} + 2) - 0 = 1 + 2 = 3 \frac{m}{s}$ $v_(0->2)=(4/4+2)-0=1+2=3m/s$

What is the average speed of an object that is still at t=0t=0t=0 and accelerates at a rate of a(t) =t/2+1a(t)=t2+1a(t) =t/2+1 from t in [0, 2]t∈[0,2]t in [0, 2]?