view policies current attempt in progress your velocity is given by v(t)=t² + 3 in m/sec, with t in seconds…
view policies current attempt in progress your velocity is given by v(t)=t² + 3 in m/sec, with t in seconds. estimate the distance, s, traveled between t = 0 and t = 5. use an overestimate with data every one second. the distance is approximately m. etextbook and media save for later
Answer
Explanation:
Step1: Identify the over - estimate method
We will use a right - hand Riemann sum. The interval is $[0,5]$ and $\Delta t = 1$.
Step2: Calculate the velocity at each right - hand endpoint
For $t = 1$, $v(1)=1^{2}+3=4$ m/sec; for $t = 2$, $v(2)=2^{2}+3 = 7$ m/sec; for $t = 3$, $v(3)=3^{2}+3=12$ m/sec; for $t = 4$, $v(4)=4^{2}+3 = 19$ m/sec; for $t = 5$, $v(5)=5^{2}+3=28$ m/sec.
Step3: Calculate the right - hand Riemann sum
The right - hand Riemann sum $R=\sum_{i = 1}^{5}v(t_{i})\Delta t$. Since $\Delta t=1$, $R=v(1)\times1 + v(2)\times1+v(3)\times1+v(4)\times1+v(5)\times1$. $R=4 + 7+12+19+28$. $R=70$.
Answer:
70