A particle started moving in a straight line from rest with a uniform acceleration of 5.4 metres per square second. Determine its velocity after two seconds from when it started moving.
We’re told this particle has a uniform, or a constant, acceleration. And so, we’re going to use the equations of constant acceleration. These are often referred to as the SUVAT equations, where SUVAT is an acronym for the variables. 𝑠 is displacement, 𝑢 is initial velocity, 𝑣 is final velocity, 𝑎 is acceleration, and 𝑡 is time. So, let’s see what we know about our particle.
The particle started moving from rest, so its initial velocity was zero. Now, this is zero metres per second here. It has a constant acceleration of 5.4 metres per square second. And we’re trying to find its final velocity, that’s 𝑣, after two seconds, so when 𝑡 is equal to two. Notice, we’re working in metres per square second and seconds, so we don’t need to do anything with our units. We’re not interested in its displacement at all. So, we need to find the equation of constant acceleration that does not include the 𝑠.
Well, that’s this first one, 𝑣 is equal to 𝑢 plus 𝑎𝑡. Let’s substitute what we know about our particle into this equation. We get 𝑣 is equal to zero plus 5.4 times two. 5.4 times two is 10.8. And since our acceleration is in metres per square second, and the time is in seconds, so velocity must be in metres per second. And so, the velocity of our particle, two seconds after it started moving, is 10.8 metres per second.