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, you can use the equation:
Acceleration (a) = (Final velocity - Initial velocity) / Time
Given:
Initial velocity (u) = 13 m/s
Final velocity (v) = 25 m/s
Time (t) = 6.0 seconds
Substituting the values into the formula:
Acceleration (a) = (25 m/s - 13 m/s) / 6.0 s
a = 12 m/s / 6.0 s
a = 2 m/s²
Therefore, the acceleration of the car is 2 m/s².
To find the distance traveled by the car in this time, you can use the equation:
Distance (s) = (Initial velocity × Time) + (0.5 × Acceleration × Time²)
Given:
Initial velocity (u) = 13 m/s
Time (t) = 6.0 seconds
Acceleration (a) = 2 m/s²
Substituting the values into the formula:
Distance (s) = (13 m/s × 6.0 s) + (0.5 × 2 m/s² × (6.0 s)²)
= 78 m + (0.5 × 2 m/s² × 36 s²)
= 78 m + (2 m/s² × 18 s²)
= 78 m + 36 m
= 114 m
Therefore, the car traveled a distance of 114 meters in this time.
Acceleration is the velocity change (12 m/s) divided by the time interval (6.0 s).
Distance travelled is the average velocity
(19 m/s in this case) multiplied by the time interval.