A truck covers 38.7 m in 6.4 s while smoothly
slowing down to a final speed of 3.5 m/s.
Find its original speed.
Answer in units of m/s
To find the original speed of the truck, we can use the equation of motion relating distance, time, initial velocity, and final velocity.
The equation is:
Distance = (Initial velocity + Final velocity) / 2 * Time
Let's substitute the given values into the equation:
38.7 m = (Initial velocity + 3.5 m/s) / 2 * 6.4 s
To solve for the initial velocity, we need to isolate it on one side of the equation. Let's start by multiplying both sides by 2:
2 * 38.7 m = (Initial velocity + 3.5 m/s) * 6.4 s
77.4 m = (Initial velocity + 3.5 m/s) * 6.4 s
Now, divide both sides by 6.4 s:
(Initial velocity + 3.5 m/s) = 77.4 m / 6.4 s
Simplifying the right side:
(Initial velocity + 3.5 m/s) = 12.09 m/s
Lastly, subtract 3.5 m/s from both sides to solve for the initial velocity:
Initial velocity = 12.09 m/s - 3.5 m/s
Initial velocity = 8.59 m/s
Therefore, the original speed of the truck was 8.59 m/s.