An automobile accelerates 1.77 m/s2 over 6.00 s to reach freeway speed at the end of the entrance ramp. If the car's final velocity is 24.44 m/s, what is it's initial speed when it began accelerating.
the answer i got was 35.06 m/s (35.1 m/s when doing sig figs). I didn't no if my answer was true?
My bad, i switched initial velocity with final velocity in my equation. I actually got 13.82 (13.8 with sig figs). Is my answer still true?
To solve this problem, we can use one of the four basic kinematic equations of motion:
\(v_f = v_i + at\)
where:
\(v_f\) = final velocity = 24.44 m/s
\(v_i\) = initial velocity (what we want to find)
\(a\) = acceleration = 1.77 m/s²
\(t\) = time = 6.00 s
Rearranging the equation, we get:
\(v_i = v_f - at\)
Now, let's substitute the given values into the equation:
\(v_i = 24.44 \, \text{m/s} - (1.77 \, \text{m/s}²)(6.00 \, \text{s})\)
\(v_i = 24.44 \, \text{m/s} - 10.62 \, \text{m/s}\)
\(v_i = 13.82 \, \text{m/s}\)
Therefore, the initial speed of the car when it began accelerating is 13.82 m/s.
To solve this problem, you can use the following kinematic equation:
v = u + at
Where:
v = final velocity
u = initial velocity (also known as initial speed)
a = acceleration
t = time
Given:
Final velocity (v) = 24.44 m/s
Acceleration (a) = 1.77 m/s^2
Time (t) = 6.00 s
We need to find the initial velocity (u). Rearranging the equation, we have:
u = v - at
Substituting the given values:
u = 24.44 m/s - (1.77 m/s^2 × 6.00 s)
= 24.44 m/s - 10.62 m/s
= 13.82 m/s
Thus, the initial speed of the car when it began accelerating is 13.82 m/s (rounded to three significant figures). Therefore, your answer of 35.06 m/s is not correct. Please recheck your calculations.