a motor travels at a constant velocity of 10 m/s for 15 seconds and then accelerates at 0.5 m/s ² for 10 seconds .
calculate the velocity of the motor car
make a neat labelled sketch of the velocity of the time graph for the motion
To calculate the velocity of the motor car, we need to find the total distance traveled during both the constant velocity phase and the acceleration phase.
In the constant velocity phase:
Velocity = 10 m/s
Time = 15 seconds
Distance = Velocity * Time = 10 m/s * 15 s = 150 meters
In the acceleration phase:
Initial velocity = 10 m/s
Acceleration = 0.5 m/s^2
Time = 10 seconds
To find the final velocity in this phase, we can use the equation: vf = vi + at
Final velocity = 10 m/s + (0.5 m/s^2 * 10 s) = 10 m/s + 5 m/s = 15 m/s
To find the distance traveled during this phase, we use the equation: d = vi * t + 0.5 * a * t^2
Distance = 10 m/s * 10 s + 0.5 * 0.5 m/s^2 * (10 s)^2
Distance = 100 m + 25 m = 125 meters
The total distance traveled is the sum of the distances in both phases:
Total distance = 150 meters + 125 meters = 275 meters
Now, to calculate the final velocity, we divide the total distance by the total time:
Total time = 15 seconds + 10 seconds = 25 seconds
Final velocity = Total distance / Total time = 275 m / 25 s = 11 m/s
The velocity of the motor car is 11 m/s.
Unfortunately, I'm unable to make a neat labelled sketch here. However, the graph should have two phases:
1. Constant velocity phase: The graph will be a straight horizontal line at 10 m/s for 15 seconds.
2. Acceleration phase: The graph will show a linear increase in velocity from 10 m/s to 15 m/s over the course of 10 seconds.