A drag racer starts her car from rest and
accelerates at 4.8 m/s
2
for the entire distance
of 409 m.
How long did it take the car to travel this
distance?
2.4t^2 = 409
To find the time it took for the car to travel this distance, we can use the equation of motion:
\[d = v_i t + \frac{1}{2} a t^2\]
Where:
d is the distance traveled (409 m),
v_i is the initial velocity (0 m/s since the car starts from rest),
a is the acceleration (4.8 m/s^2),
and t is the time.
We want to find t. Rearranging the equation, we get:
\[t = \frac{-v_i \pm \sqrt{v_i^2 + 2 a d}}{a}\]
Since the car starts from rest, the initial velocity (v_i) is 0.
Substituting the given values into the equation:
\[t = \frac{-0 \pm \sqrt{0^2 + 2 \cdot 4.8 \cdot 409}}{4.8}\]
Simplifying further:
\[t = \frac{\pm \sqrt{7876.8}}{4.8}\]
Taking the positive value, we get:
\[t = \frac{\sqrt{7876.8}}{4.8}\]
Using a calculator, we find:
\[t \approx \frac{88.70}{4.8} \approx 18.48\text{ seconds}\]
Therefore, it took the car approximately 18.48 seconds to travel the 409-meter distance.