Question Video: Calculating Acceleration from Change in Speed and Time Science

A car starts accelerating uniformly from rest. After accelerating for 3 seconds, the car has a speed of 18 meters per second. What is the acceleration of the car?

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Video Transcript

A car starts accelerating uniformly from rest. After accelerating for three seconds, the car has a speed of 18 meters per second. What is the acceleration of the car?

Let’s say that this dot here is our car. And if we start counting time at zero seconds, we know that at that start since the car begins from rest, it has a speed of zero meters per second. But then, three seconds later, we’re told that the car has a speed of 18 meters per second. To begin solving for acceleration, let’s recall the mathematical equation for acceleration. The acceleration 𝑎 of an object equals its final speed, we’ll call it 𝑣 two, minus its initial speed all divided by the amount of time it takes for the object to change speeds from 𝑣 one to 𝑣 two.

In our case, the initial speed of the object 𝑣 one is zero meters per second, 𝑣 two is 18 meters per second, and the change in time over which this change in speed happens is three seconds minus zero seconds or simply three seconds. So then, here’s what the equation for our object’s acceleration looks like: 18 meters per second minus zero meters per second is 18 meters per second. And 18 divided by three is six. So when we simplify our units, we get an answer of six meters per second squared. This is the acceleration of the car.