The speed time graph shows the motion of a car over a period of 40 seconds.
a. describe the motion of the car between:
1.) O and A - The car is traveling at constant speed from 0 to 20 m/s.
2.) A and B - The car is at rest for 20 seconds.
3.) B and C - The car is decelerating at 20 m/s.
b. Calculate the acceleration of the car.
c. Calculate the distance the car traveled at constant speed.
d. What is the average speed of the car for the whole journey?
20 m/s is not a deceleration rate
What is initial speed of the car
a.
1.) O and A - The car is traveling at a constant speed from 0 to 20 m/s. This means that the car is accelerating uniformly, maintaining the same rate of increase in speed over time.
2.) A and B - The car is at rest for 20 seconds. This means that the car is not moving and its speed remains constant at 0 m/s.
3.) B and C - The car is decelerating at 20 m/s. This means that the car is slowing down uniformly, decreasing its speed by 20 m/s over the given time interval.
b. To calculate the acceleration of the car, we need to divide the change in velocity by the change in time. Looking at the graph, we can see that the car's initial velocity is 20 m/s, and its final velocity is 0 m/s. The time it takes for the car to decelerate from 20 m/s to 0 m/s is 20 seconds.
Acceleration = (change in velocity) / (change in time)
Acceleration = (0 m/s - 20 m/s) / (20 s)
Acceleration = (-20 m/s) / (20 s)
Acceleration = -1 m/s²
Therefore, the acceleration of the car is -1 m/s².
c. To calculate the distance the car traveled at a constant speed, we need to find the area under the section of the graph where the car is traveling at a constant speed. In this case, the area under the graph is represented by a rectangle:
Length of rectangle = 20 m/s (constant speed)
Width of rectangle = 20 s (time interval from O to A)
Distance = length × width
Distance = 20 m/s × 20 s
Distance = 400 meters
Therefore, the car traveled a distance of 400 meters at a constant speed.
d. To calculate the average speed of the car for the whole journey, we need to find the total distance traveled divided by the total time taken. From the graph, we can see that the total distance traveled is 400 meters and the total time taken is 40 seconds.
Average Speed = Total Distance / Total Time
Average Speed = 400 meters / 40 seconds
Average Speed = 10 m/s
Therefore, the average speed of the car for the whole journey is 10 m/s.
a.
1.) O and A: The car is traveling at a constant speed from 0 to 20 m/s. This means that during this time, the car maintains a constant velocity with no change in speed or direction. It covers a distance of 20 meters in this period.
2.) A and B: The car is at rest for 20 seconds. This means that the car is not moving during this time. It remains stationary with a speed of 0 m/s.
3.) B and C: The car is decelerating at 20 m/s. This means that the speed of the car is decreasing by 20 m/s. The car is slowing down during this time.
b. To calculate the acceleration of the car, we can use the formula:
acceleration = (change in velocity) / (time taken)
In this case, the change in velocity is -20 m/s (since the car is decelerating), and the time taken is 40 seconds.
acceleration = (-20 m/s) / (40 s) = -0.5 m/s²
So, the acceleration of the car is -0.5 m/s².
c. To calculate the distance the car traveled at constant speed, we can use the formula:
distance = speed × time
In this case, the speed is 20 m/s and the time is 20 seconds.
distance = 20 m/s × 20 s = 400 meters
So, the car traveled a distance of 400 meters at constant speed.
d. The average speed of the car for the whole journey can be calculated by dividing the total distance traveled by the total time taken.
Total distance traveled = distance traveled at constant speed + distance traveled while decelerating
= 400 meters + 0 meters (since the car is not moving while decelerating)
= 400 meters
Total time taken = 40 seconds
average speed = total distance traveled / total time taken
= 400 meters / 40 seconds
= 10 meters per second
So, the average speed of the car for the whole journey is 10 meters per second.