What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?

Video transcript

Hey, everyone. Welcome back in this problem. A rally car driver is performing a drill. We're asked to find the uniform acceleration Of the car that will speed it up from zero mph to mph within five seconds and were asked to give the answer in SI units. The answer choices were given are a 6m/s squared. B 13.4 m per second squared, C 161 m per second squared and D 2.68 m per second squared. Now, we're looking for a uniform acceleration that indicates that we can use our new AM equations, uniform accelerated motion equations or the Kinnah Matic equations if that's what your textbook calls them. So let's go ahead and write out the five variables and fill in the information. We know We have that the initial speed v naught is equal to zero mph. We know that the final speed V F is equal to 30 MPH. Okay. The car speeds up from 0 to 30 MPH. We know that the time this takes is five seconds. We're asked to find the acceleration A and we aren't given any information about the distance or the displacement of this car. All right, we have three values V, not V F and T, we're looking for the acceleration A. So we can do this, we can go ahead and choose the equation that includes those four variables plug in our values and away we go. Now, before we do that, we're asked to give the answer in S I units. So let's go ahead and convert our speeds into S I units of meters per second before we substitute him. So the first one is simple, the speed, zero MPH is going to be zero m per second. Okay, you have no speed. You're not moving regardless of what unit you use. Now, when we look at 30 mph, We can write this as 30 with a unit mile divided by our, we know that in every hour There is 3600 seconds. So we multiply by one hour divided by seconds, the unit of our divides out, We can multiply again by 1,609.3, 4, 4 m divided by mile because that's the number of meters per mile we're essentially doing every time we multiply by one of these factors, the new reader and denominator are equivalent. So we're essentially multiplying by one which doesn't change the value we had. Now, when we do this, the unit of mile will divide out and we're left with just a unit of meters per second, which is what we want. We have 30 divided by 3600 times 1609.344, which gives us a speed of 13.4112 meters per second. All right. So we have our variables in R S I units. Let's go ahead and choose that equation we want to use again. We're going to choose the equation without delta X in it since we aren't given information about that. And that's not what we're asked to find. We have V F is equal to V naught plus A multiplied by T substituting in our values, we have 13.4112 m per second is equal to, we have zero m per second plus the acceleration a multiplied by the time five seconds. And so the acceleration A is going to be equal to 13.4112 m per second, divided by five seconds meters per second over second, gives us meters per second squared for the unit, which is what we want for acceleration may get a value of 2.68, 2-4 m/s squared. And that's that acceleration, that uniform acceleration of that driver that we were looking for. Now, we can see that the answer choices round to three significant digits. So we used three significant digits, our answer is going to be 2.68 m per second squared that corresponds with answer choice D thanks everyone for watching. I hope this video helped see you in the next one.