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?
I don't understand
a.
1.) O and A - The car is traveling at a constant speed from 0 to 20 m/s. This means that the car's speed remains the same throughout this time interval. The car is accelerating during this interval because its velocity is increasing.
2.) A and B - The car is at rest for 20 seconds. This means that the car's speed is 0 m/s. It is not moving during this time interval.
3.) B and C - The car is decelerating at 20 m/s. This means that the car's speed is decreasing at a rate of 20 m/s. It is slowing down during this time interval.
b. To calculate the acceleration of the car, we need to use the formula:
acceleration = (change in velocity) / (change in time)
In this case, the car goes from 0 m/s at point A to 20 m/s at point B over a time interval of 20 seconds.
acceleration = (20 m/s - 0 m/s) / (20 s - 0 s)
acceleration = 20 m/s / 20 s
acceleration = 1 m/s²
So, the acceleration of the car is 1 m/s².
c. To calculate the distance the car traveled at constant speed, we need to use the formula:
distance = speed × time
In this case, the car traveled at a constant speed of 20 m/s for a time interval of 20 seconds.
distance = 20 m/s × 20 s
distance = 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.
The total distance traveled is 400 meters (from part c) and the total time taken is 40 seconds (given in the question).
average speed = total distance / total time
average speed = 400 meters / 40 seconds
average speed = 10 m/s
So, the average speed of the car for the whole journey is 10 m/s.
a. describe the motion of the car between:
1.) O and A - The car is traveling at a constant speed from 0 to 20 m/s.
To describe the motion of the car between O and A, we can say that the car is moving at a constant speed of 20 m/s. This means that it covers equal distances in equal intervals of time. The slope of the speed-time graph in this region is linear and positive, indicating a constant speed.
2.) A and B - The car is at rest for 20 seconds.
To describe the motion of the car between A and B, we can say that the car comes to a rest and remains stationary for 20 seconds. This is indicated by a horizontal line at zero speed on the speed-time graph.
3.) B and C - The car is decelerating at 20 m/s.
To describe the motion of the car between B and C, we can say that the car is decelerating. Deceleration means a decrease in speed. The slope of the speed-time graph in this region is linear and negative, indicating a decrease in speed. The magnitude of the slope (-20 m/s) indicates that the car is decelerating at a rate of 20 m/s.
b. Calculate the acceleration of the car.
Acceleration is defined as the rate of change of velocity. Since the speed-time graph shows speed and not velocity, we need to convert the information into velocity-time graph to calculate acceleration.
To do this, we can draw a new graph representing the velocity-time relationship. The velocity would be the slope of the speed-time graph, and acceleration would be the slope of the velocity-time graph.
Using the given information, we can see that the velocity from O to A is constant and equal to 20 m/s. So, the velocity-time graph would be a horizontal line at 20 m/s.
Since the velocity is constant, the acceleration would be zero. So, the acceleration of the car is zero.
c. Calculate the distance the car traveled at constant speed.
To calculate the distance traveled, we need to find the area under the speed-time graph between O and A.
In this case, the speed is constant at 20 m/s for a duration of 20 seconds. The area of a rectangle is given by the product of its base (20 seconds) and height (20 m/s).
So, the distance traveled at constant speed is 20 m/s x 20 seconds = 400 meters.
d. What is the average speed of the car for the whole journey?
To calculate the average speed, we need to divide the total distance traveled by the total time taken.
From the graph, we can see that the car covers a distance of 400 meters during a total time of 40 seconds.
So, the average speed of the car for the whole journey is 400 meters / 40 seconds = 10 m/s.