At highway speeds, a particular automobile is capable of an acceleration of about $1.8 \textrm{ m/s}^2$. At this rate, how long does it take to accelerate from 65 km/h to 120 km/h?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Acceleration is the change in velocity over time and we can rearrange this to solve for time. So we'll multiply both sides by t and divide both sides by a and we end up with t appearing on the left and a disappearing on the left and there a is on the bottom on the right. So we have t is the change in velocity over acceleration. So the change in velocity is final velocity minus initial velocity divide that by acceleration. So first we have to convert all these into consistent units so we need mks—meters, kilograms, seconds. So we'll change these kilometers per hour into meters per second; 120 kilometers per hour times 1 hour for every 3600 seconds times a 1000 meters per kilometer and we'll have the hours canceling and the kilometers canceling and this multiplied by a 1000 divided by 3600 is the same as dividing by 3.6—that's what I have done in the calculator over here. So that's 33.33 meters per second and same story with the initial velocity of 65 kilometers an hour turns into 18.06 meters per second and so the time will be the change in velocity; final—33.33 meters per second—minus initial—18.06 meters per second— divided by the acceleration of 1.8 meters per second squared giving us a time of 8.5 seconds to get from 65 kilometers an hour up to 120 kilometers an hour.