A car accelerates at a constant rate from 13m/s to 25m/s in 6.0seconds. What was its acceleration? How far did it travel in this time?
To find the acceleration of the car, we can use the formula:
Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)
The change in velocity is the difference between the final velocity (v2) and the initial velocity (v1):
Δv = v2 - v1
Substituting the given values into the formula:
Δv = 25 m/s - 13 m/s
Δv = 12 m/s
The time taken is given as 6.0 seconds.
Now we can calculate the acceleration:
a = Δv / Δt
a = 12 m/s / 6.0 s
a = 2.0 m/s²
Therefore, the acceleration of the car is 2.0 m/s².
To find the distance traveled by the car during this time, we can use the kinematic equation:
Distance (d) = Initial velocity (v1) * Time taken (Δt) + 0.5 * Acceleration (a) * Time taken (Δt)²
Substituting the values given:
d = 13 m/s * 6.0 s + 0.5 * 2.0 m/s² * (6.0 s)²
d = 78 m + 0.5 * 2.0 m/s² * 36 s²
d = 78 m + 36 m
d = 114 m
Therefore, the car traveled a distance of 114 meters during this time.