{Use of Tech} Decreasing velocity A projectile is fired upwa...

Question

{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity (in m/s) is given by v(t) = 200 / √t+1, for t≥0.

a. Graph the velocity function, for t≥0.

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a projectile is launched upwards with a velocity in meters per second given by VFT, which is equal to 400 multiplied by the square root of the quantity of T plus 1 in quantity. Draw the graph of the acceleration function using a graphing calculator when T is greater than or equal to 0. So this problem wants us to graph the acceleration function. And so, first thing we need to do is actually determine what that is. So recall that the acceleration is equal to the time derivative of our velocity function. That means our acceleration, AFT. It's going to be equal to the derivative with respect to T. Of VFT. Now we're given an expression for our velocity in the problem, so we'll substitute that in, but this is going to be equal to the derivative with respect to T. Of the quantity of 400 multiplied by the quantity of T + 1 in quantity raised to the 12 power in quantity. So here we've rewritten the square root as raising the quantity to the 12 power. And the reason why we did this, it'll make it a little easier to take this derivative. So to take this derivative, we'll need to use our constant multiple rule, our power rule, and our chain rule. So using all three of those, this is going to be equal to. 400 Multiplied by 1/2, multiplied by the quantity of T + 1 in quantity, raised to the minus 1/2 hour, multiplied by 1, where the one here is due to the chain rule. And we can simplify this expression, and this is going to be equal to 200. Divided by the square root of the quantity of T + 1. So this is the function that we need to plot using our graphing calculator. And so doing so, we will get to the graph that we see on the screen, where we have our acceleration as a function of time in meters per second squared on the Y axis and T in seconds on the X-axis. So, our acceleration starts at a value of 200 when T is equal to 0. It decreases rapidly and slowly approaches 0 as T approaches infinity. So this is the graph that the problem was asking for. So this here is the final answer for the question. So I hope that this explanation has been useful, and I'll see you in the next video.

​​{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity (in m/s) is given by v(t) = 200 / √t+1, for t≥0.a. Graph the velocity function, for t≥0.

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{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity (in m/s) is given by v(t) = 200 / √t+1, for t≥0.
a. Graph the velocity function, for t≥0.