) A toy race car zooms across the ground with an acceleration of 2.8 m/s^2. After 4 seconds it has a final velocity of 22.2 m/s, what is the toy car's initial velocity? show work
We can use the equation of motion to solve this problem:
v = u + at
where:
v = final velocity = 22.2 m/s
u = initial velocity (what we need to find)
a = acceleration = 2.8 m/s^2
t = time taken = 4 s
Rearranging the equation, we get:
u = v - at
Substituting the given values:
u = 22.2 m/s - 2.8 m/s^2 * 4 s
Simplifying the equation, we have:
u = 22.2 m/s - 11.2 m/s
u = 11 m/s
Therefore, the toy car's initial velocity is 11 m/s.
To find the initial velocity of the toy car, we can use the following equation:
vf = vi + at
Where:
vf = final velocity = 22.2 m/s
vi = initial velocity (what we need to find)
a = acceleration = 2.8 m/s^2
t = time = 4 seconds
Now, let's plug in the given values into the equation and solve for vi:
22.2 m/s = vi + (2.8 m/s^2)(4 s)
To isolate vi, we need to get rid of the term (2.8 m/s^2)(4 s). To do this, we can find the value of (2.8 m/s^2)(4 s) and subtract it from both sides of the equation:
(2.8 m/s^2)(4 s) = 11.2 m/s
22.2 m/s - 11.2 m/s = vi
Therefore, the initial velocity of the toy car is:
vi = 11 m/s
To find the toy car's initial velocity, we can use the formula:
Final velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t)
In this case, the final velocity (v) is 22.2 m/s, the acceleration (a) is 2.8 m/s^2, and the time (t) is 4 seconds. We need to isolate the initial velocity (u) in the equation.
Rearrange the formula to solve for Initial velocity (u):
u = v - a * t
Now, substitute the values:
u = 22.2 m/s - 2.8 m/s^2 * 4 s
Next, perform the multiplication:
u = 22.2 m/s - 11.2 m/s
Now, subtract:
u = 11 m/s
Therefore, the toy car's initial velocity is 11 m/s.