What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - \frac{t^{2}}{4}$ $a(t) =5-t^2/4$ on $t \in [2, 4]$ $t in [2,4]$ ?

Question

What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - \frac{t^{2}}{4}$ $a(t) =5-t^2/4$ on $t \in [2, 4]$ $t in [2,4]$ ?

1 Answer

Impact of this question

1953 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-18T01:34:04

$average speed = 12.5$ $"average speed" = 12.5$ $m/s$ $"m/s"$

Explanation:

We're asked to find the average speed of a particle over a time interval, given its acceleration as a function of time.

The equation for average speed is

$average speed = \frac{distance traveled}{time interval}$ $"average speed" = "distance traveled"/"time interval"$

Position is the second integral of acceleration. The total distance traveled is different from the displacement because it is strictly positive. Therefore, to find the distance traveled from $t \in [2 l s, 4 l s]$ $t in [2color(white)(l)"s", 4color(white)(l)"s"]$ , we take the absolute value (so that it is positive) of the definite integral from $2$ $2$ to $4$ $4$ :

$"distance traveled" = int_2^4intcolor(white)(l)|5-(t^2)/4|color(white)(l)dtcolor(white)(l)dt = color(red)(ul(25color(white)(l)"m"$

The time interval is $2$ $"s"$ , so we have

$color(blue)("average speed") = (color(red)(25color(white)(l)"m"))/(2color(white)(l)"s") = color(blue)(ulbar(|stackrel(" ")(" "12.5color(white)(l)"m/s"" ")|)$

Science

Math

Humanities

... and beyond

What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - \frac{t^{2}}{4}$ $a(t) =5-t^2/4$ on $t \in [2, 4]$ $t in [2,4]$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the average speed of an object that is not moving at t=0t=0t=0 and accelerates at a rate of a(t) =5-t^2/4a(t)=5−t24a(t) =5-t^2/4 on t in [2,4]t∈[2,4]t in [2,4]?

1 Answer

Explanation:

Related questions

Impact of this question

What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - \frac{t^{2}}{4}$ $a(t) =5-t^2/4$ on $t \in [2, 4]$ $t in [2,4]$ ?