Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume...

Question

Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume v(0)=0, s(0)=0, and t is measured in seconds.

d. How long does it take the racer to travel 300 ft?

Accepted Answer

Welcome back, everyone. A car accelerates at A of T equals 72 ft per second squared. Assume B of 0 equals 0, S of 0 equals 0, and T is in seconds. How long does it take the car to travel 180 ft? A 2 seconds, B square root of 2 seconds. C 5 seconds, and D square root of 5 seconds. For this problem, we are going to identify the position function. Starting with the acceleration function, we have to recall that first of all, we can identify our velocity function by integrating the acceleration function. So we're integrating 72 with respect to time. This is equal to 72 T plus a constant of integration C. And then we can use the initial condition V of 0 equals 0, which means that if T is 0, V becomes 0 as well. So we set an equation 0 equals 722 multiplied by 0 + C. And therefore our constant of integration, let's call it C1. It's equal to 0. So now we can define our velocity function as 702 T. Measured in feet per second. From here, we can evaluate our position function as of T, which is the integral of the velocity function. So now we're integrating 70 to TDT. We can factor out the constant and integrate CDT using the power rule, which would be T2d divided by 2. And we're adding a constant of integration C2. This is equal to 36 T2 plus C2. And now let's use the initial conditions of 0 equals 0. So 0 equals 36 multiplied by 0 squad + C2. And from here we can show that C2 is 0 as well. So that our position function becomes 36 T squad. Now, notice that 36 T squared is always non-negative, so our position function. Allows us to calculate both displacement and distance that would have exactly same value, right? Therefore, if we want to Consider 180 ft, which is our distance, we can use our position function. Specifically, we're going to set S of T equals 180 ft. And this means that 36 T squared. Is equal to 180. We're going to solve for time dividing both sides by 36. We got time squared. Equals 180. Divided by 36, which is 5. So now time is equal to square root of. 5 and specifically we have T time values because square root of T2 is positive or negative. Square root of 5 in this case. Because time cannot be negative, we can conclude that there is only one solution, T equals square root of 5 seconds, which corresponds to the answer choice D. Thank you for watching.

Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume v(0)=0, s(0)=0, and t is measured in seconds.d. How long does it take the racer to travel 300 ft?

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Acceleration A drag racer accelerates at a(t)=88 ft/s². Assume v(0)=0, s(0)=0, and t is measured in seconds.

d. How long does it take the racer to travel 300 ft?