Question

A car is initially moving with a velocity of 3 m/s. then it accelerates uniformly at the rate of 0.6 m/s^2 for 5 seconds. What is the distance traveled by the car in 5 seconds?

Answer 1

Ok so you could use the formula for distance (s):\[s=v_{i}t+\frac{ 1 }{ 2 }at^2\]
Where vi is the initial velocity,t the time, and a the acceleration.
So plug in the values they gave you:
3m/s for vi,5 seconds for t, and 0.6 m/s^2 for a. :
\[distance=(3 m/s)( 5s)+\frac{ 1 }{ 2 }(0.6 m/s^2)(5 s)^2\]
You know that this will end up in meters because you are solving for distance so don't worry about multiplying the "units" just multiply the numbers using a calculator or your brain. I will show you with my brain:\[distance = 15m+\frac{ 1 }{ 2 }(0.6 m/s^2)(5 s)^2\]
I multiplied the 3 m/s and 5
Next:\[distance= 15m+\frac{ 1 }{ 2 }(0.6 m/s^2)(25s^2)\]
I squared the 5 seconds
Next:\[distance=15m+\frac{ 1 }{ 2 }(15m)\]
I multiplied the 0.6 m/s^2 and 25 s^2
Next:\[distance = 15m+7.5m\]
I found 1/2 of the "second" 15 meters
Finally:\[distance = 22.5 m\]
I added the two terms together!

We get distance = 22.5 meters!

ANSWER: 22.5 METERS!