CALC. A car's velocity as a function of time is given by v_x(t) = α + βt^2, where α = 3.00 m/s and β = 0.100 m/s^3. (a) Calculate the average acceleration for the time interval t = 0 to t = 5.00 s.

Video transcript

Welcome back everybody. We are making observations about a squirrel that is running along the ground around the forest. We are given the velocity of the squirrel as a function of time. According to this function right here, Alpha, which is equal to 4.5 plus beta which were given as 0.27 times t squared. And we are looking at an interval where the starting time is zero seconds and the final time is 12 seconds. And we are tasked with finding what is the squirrels. Average acceleration over this time? Well, we have a function for this. This is just going to be equal to the change in velocity over the change in time which is equal to our final velocity minus our initial velocity divided by our final time minus our initial time. What we have these bottom terms down here, But how are we going to find these top terms up here? What we do is we just plug in these times into our formula for velocity to find our initial and final velocities. So let's go ahead and do that first. I want to start out with our initial velocity. This is just going to be equal to us. Plugging in zero into our equation. This gives us 4.5 plus 0.27 times zero squared. This whole term goes away and this gives us 4.5 m per second. Great! Now what about our final velocity? Well, all we do is just plug in our final time of 12 seconds and we get 4.5 plus 0.27 times 12 squared. Which one? We plug into our calculator. We get 43.38 m per second. Now we are ready to use our equation right here to find the average acceleration. So we have that our average acceleration is equal to 43. -4.5, divided by 12 0, giving us a final answer choice of 2.865 m/s squared or answer choice. C Thank you all so much for watching. Hope this video helped. We will see you all in the next one.