Question

005 10.0 points
a 500 - kilogram sports car accelerates uniformly from rest, reaching a speed of 30 meters per second in 6 seconds.
what distance has the car traveled during the 6 seconds?

1. 90 m
2. 180 m
3. 15 m
4. 60 m
5. 30 m

Explanation:

Step1: Find the acceleration

The car starts from rest ($u = 0\ m/s$), final velocity $v=30\ m/s$ and time $t = 6\ s$. Using the formula $v=u + at$, we can find acceleration $a$. Since $u = 0$, $a=\frac{v - u}{t}=\frac{30-0}{6}=5\ m/s^{2}$.

Step2: Calculate the distance

We use the second - equation of motion $s=ut+\frac{1}{2}at^{2}$. Since $u = 0\ m/s$, the equation simplifies to $s=\frac{1}{2}at^{2}$. Substituting $a = 5\ m/s^{2}$ and $t = 6\ s$, we get $s=\frac{1}{2}\times5\times6^{2}=\frac{1}{2}\times5\times36 = 90\ m$.

Answer:

1. 90 m