# Video: Rate of Velocity Change

A cyclist accelerates at 2.3 m/s². How much time is needed for the cyclist to increase their velocity by 9.43 m/s?

02:00

### Video Transcript

A cyclist accelerates at 2.3 meters per second squared. How much time is needed for the cyclist to increase their velocity by 9.43 meters per second?

Okay, so in this question, we’ve been told that we’ve got a cyclist who is accelerating at 2.3 meters per second squared. We need to work out the amount of time needed by the cyclist to increase their velocity by 9.43 meters per second. Let’s start by labelling some quantities.

Firstly, we’ve been told that the acceleration of the cyclist, which we’ll call 𝑎, is 2.3 meters per second squared. Secondly, we know that the velocity increase of the cyclist must be 9.43 meters per second and we’ll call this quantity Δ𝑣. The reason that we’re calling that Δ𝑣 is because Δ usually represents a change. And we’ve been told that the velocity of the cyclist must increase by 9.43 meters per second. Therefore, this is a change in the cyclist’s velocity: if it’s increasing, the velocity is changing. Now, finally, what we need to work out is the amount of time taken for this to occur. We’ll call this 𝑡.

To work out the time 𝑡, we need to recall the relationship between acceleration, change in velocity, and time. Specifically, we need to recall that acceleration is defined as the change in velocity of an object divided by the time taken for that velocity change to occur.

Now, in this situation, we’re trying to work out the value of 𝑡. So we need to rearrange the equation. We do this by multiplying both sides of the equation by 𝑡 over 𝑎. This way the acceleration cancels on the left-hand side and the time cancels on the right. What we’re left with then is that the time taken for a velocity change to occur is equal to the velocity change in question divided by the acceleration.

Now, at this point, we can substitute in the values on the right-hand side of the equation. We find that the time 𝑡 is equal to the change in velocity, which is 9.43 meters per second, divided by the acceleration, which is 2.3 meters per second squared. Now, we can evaluate the right-hand side of the equation to give us a value for 𝑡.

At this point, we’ve arrived at our final answer: the time needed for the cyclist to increase their velocity by 9.43 meters per second is 4.1 seconds.