a) To find the acceleration of the car in m/s², we need to convert the final velocity from km/h to m/s and use the formula for acceleration:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Given: Initial Velocity (u) = 0 km/h Final Velocity (v) = 75 km/h Time (t) = 15 seconds
Converting velocities from km/h to m/s: Initial Velocity (u) = 0 km/h = 0 m/s Final Velocity (v) = 75 km/h = (75 * 1000) / 3600 m/s = 20.83 m/s
Now, we can calculate the acceleration: Acceleration (a) = (Final Velocity - Initial Velocity) / Time a = (20.83 m/s - 0 m/s) / 15 s a ≈ 1.39 m/s²
Therefore, the acceleration of the car is approximately 1.39 m/s².
b) To find the position of the car when it reaches a velocity of 75 km/h, we need to calculate the distance traveled using the formula:
Distance (s) = (Initial Velocity * Time) + (0.5 * Acceleration * Time²)
Given: Initial Velocity (u) = 0 m/s Final Velocity (v) = 75 km/h = 20.83 m/s Time (t) = 15 seconds Acceleration (a) = 1.39 m/s² (from part a)
Plugging in the values: Distance (s) = (0 * 15) + (0.5 * 1.39 * 15²) s = 0 + (0.5 * 1.39 * 225) s = 0 + 156.375 s ≈ 156.375 meters
Therefore, the position of the car when it reaches a velocity of 75 km/h is approximately 156.375 meters.