In the first scenario, where the car travels at a constant speed of 60 km/h for 2 hours, we can use the formula:
Distance = Speed × Time
Distance = 60 km/h × 2 hours
Distance = 120 km
Therefore, the car travels a distance of 120 km in this scenario.
In the second scenario, where the car accelerates uniformly from rest to a speed of 60 km/h in ten seconds, we need to calculate the distance using the formula for uniformly accelerated motion:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)
Given: Initial Velocity (u) = 0 km/h (starting from rest) Final Velocity (v) = 60 km/h Time (t) = 10 seconds
First, we need to convert the velocities to meters per second (m/s) since the formula uses SI units:
Initial Velocity (u) = 0 km/h = 0 m/s Final Velocity (v) = 60 km/h = 60 × (1000/3600) m/s ≈ 16.67 m/s
Now we can calculate the acceleration (a) using the formula:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Acceleration (a) = (16.67 m/s - 0 m/s) / 10 s
Acceleration (a) = 1.67 m/s^2
Next, we can substitute the values into the formula for distance:
Distance = (0 m/s × 10 s) + (0.5 × 1.67 m/s^2 × (10 s)^2)
Distance = 0 + (0.5 × 1.67 m/s^2 × 100 s^2)
Distance = 0 + 0.5 × 1.67 m/s^2 × 100 s^2
Distance = 0 + 0.5 × 1.67 m/s^2 × 100 s^2
Distance = 0 + 0.5 × 1.67 m × 100
Distance ≈ 83.5 meters
Therefore, in this case, the car travels a distance of approximately 83.5 meters.