A car starts from rest and accelerates for 8.7 s
with an acceleration of 4.4 m/s
2
.
How far does it travel?
Answer in units of m.
d = 1/2 * a * t^2
To find the distance traveled by the car, we can use the formula:
\[ s = \frac{1}{2} \cdot a \cdot t^2 \]
where:
s = distance traveled
a = acceleration
t = time
Given:
a = 4.4 m/s^2
t = 8.7 s
Plugging in these values into the formula, we get:
\[ s = \frac{1}{2} \cdot (4.4 \, \text{m/s}^2) \cdot (8.7 \, \text{s})^2 \]
Calculating this expression we find:
\[ s = \frac{1}{2} \cdot (4.4 \, \text{m/s}^2) \cdot (75.69 \, \text{s}^2) \]
\[ s = 165.7386 \, \text{m}^2/\text{s} \]
Therefore, the car travels a distance of approximately 165.74 meters.
To find the distance traveled by the car, we can use the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time^2
Given:
Initial velocity (u) = 0 m/s (as the car starts from rest)
Acceleration (a) = 4.4 m/s^2
Time (t) = 8.7 s
Plugging in the values into the equation, we get:
distance = 0 * 8.7 + (1/2) * 4.4 * (8.7)^2
Simplifying the equation:
distance = 0 + (1/2) * 4.4 * 75.69
distance = 0 + 2.2 * 75.69
distance = 166.518
Therefore, the car travels a distance of approximately 166.518 meters.