Video Transcript
A body started moving in a straight
line with an initial velocity of 79.2 kilometers per hour and a constant
deceleration of 12.1 meters per second squared. Find the distance covered by the
body until it stopped.
To answer this question, we will
use our equations of uniform acceleration, often known as the SUVAT equations. 𝑠 is the displacement of the body,
𝑢, the initial velocity, 𝑣, the final velocity, 𝑎, the acceleration, and 𝑡, the
time. We are told that the initial
velocity is 79.2 kilometers per hour. The body is decelerating at 12.1
meters per second squared. Therefore, 𝑎 is equal to negative
12.1. We want to calculate the distance
until the body stops. Therefore, 𝑣 is equal to zero
kilometers per hour and we are trying to calculate 𝑠.
We notice that the units for
velocity and acceleration are different. The velocity is in kilometers per
hour, whereas the acceleration is in meters per square second. There are 1000 meters in one
kilometer. There are 60 seconds in a minute
and 60 minutes in an hour. Therefore, there are 3600 seconds
in one hour. To convert from kilometers per hour
to meters per second, we need to multiply by 1000 and then divide by 3600. This is the same as dividing by
3.6. And 79.2 divided by 3.6 is 22. The initial velocity is 22 meters
per second, and the final velocity is zero meters per second.
We can now use the equation 𝑣
squared is equal to 𝑢 squared plus two 𝑎𝑠 to calculate our value of 𝑠. Substituting in our values, we have
zero squared is equal to 22 squared plus two multiplied by negative 12.1 multiplied
by 𝑠. 22 squared is 484, so zero is equal
to 484 minus 24.2𝑠. This could be simplified to 24.2𝑠
is equal to 484. Dividing by 24.2 gives us 𝑠 is
equal to 20. The distance covered by the body
until it stopped is, therefore, equal to 20 meters.
