What is the deceleration of a rocket sled if it comes to rest in 1.10 seconds from a speed of 1000.0 kilometres per hour?
Let’s call this deceleration, which is another way of saying negative acceleration, 𝑎. We can begin by recalling the relationship between acceleration speed and time. An object’s acceleration is defined as its change in velocity Δ𝑣 divided by its change in time Δ𝑡. Applying this relationship to our scenario, the change in the rocket sled’s speed is 1000.0 kilometres per hour since it ends up at rest. And its change in time Δ𝑡 is given as 1.10 seconds.
Looking at the units of these values, we see we’ll want to convert the units of the numerator into meters per second. So let’s do that now. We have a value in units of kilometres per hour and we want to convert that to units of metres per second. We can recall that one kilometre is equal to 1000 meters so that we can rewrite the numerator of our fraction: 1.00 times 10 to the sixth metres.
We then recall that in one hour, there are 3600 seconds. So we can replace the hour in the denominator with 3600 seconds. Now that we’ve converted the initial speed of the rocket sled to something in units of metres per second, we can replace the numerator in our equation for acceleration with this revised term.
Notice that if we multiply these two fractions together, the final units are metres per second squared — the units of acceleration. When we perform this multiplication, we find a value of 253 meters per second squared. This is the amount that the rocket sled decelerates as it comes to rest.