A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the magnitude of the jet's acceleration, assuming it to be a constant acceleration?

Video transcript

Hey everyone in this problem, a motorcyclist riding at a constant speed of 60 km/h on the highway applies a constant acceleration for two km until he reaches a speed of 80 km/h. And were asked to determine the motorcycles acceleration. The answer choices were given are a 175 kilometers per hour squared. B 350 kilometers per hour squared, C 700 kilometers per hour squared and D 1400 kilometers per hour squared. Now we're told that this is a constant acceleration. What that means is we can use our UAM equations or arc idiomatic equations if that's what you call them. So let's write out the variables involved the initial speed while the motorcyclist is riding at 60 km/h, The final speed will they accelerate and make it to a speed of 80 km/h. The distance they travel in that acceleration is two km and the acceleration. Well, we don't know that's what we want to find out. We also aren't given any information about the time teeth. So we have three known variables were asked to find 1/4 this is just a straightforward cinematics problem. We're gonna choose the equation without time because we don't have information about the time. And that's not what we're trying to find. We get the following V F squared is equal to V naught squared plus two A delta X. The answer traces were given the acceleration is in kilometers per hour squared. And so we can leave our speeds in kilometers per hour and our distance in kilometers. So our final speed, 80 kilometers per hour, all squared is equal to our initial speed, 60 kilometers per hour, all squared plus two times the acceleration. A we're looking for times delta acts which is the same as the distance d two kilometers. So on the left hand side, we have 6400 kilometers squared per hour squared. And on the right hand side, we have 3600 kilometers squared per hour squared plus four kilometers times the acceleration we want to isolate A and so our acceleration A is going to be, we're going to subtract this 3600 kilometers squared per hour squared from the right hand side, move it to the left hand side. So we get 6400 kilometers squared per hour squared minus kilometers squared per hour squared. And then we need to divide by the four kilometers in terms of units, we have kilometers squared per hour square divided by kilometers. So one of these kilometers is going to cancel and we're gonna be left with kilometers per hour squared, which is the units for acceleration that we want from our answer choices. And when we work this out, we're gonna get an acceleration of 700 kilometers per hour squared. Alright. So looking at our answer choices, we found an acceleration for the motorcycle of 700 km/h squared. That's going to correspond with answer choice C that's it for this one. Thanks everyone for watching. See you in the next video.