Can the size of an object's displacement be greater than the distance the object travels?
Describe the motion represented by a horizontal line on a distance-time graph.
Explain whether, during a trip, a car's instantaneous speed can ever be greater than its average speed.
You are walking toward the back of a bus that is moving forward with a constant velocity. Describe your motion relative to the bus and relative to a point on the ground.
A car travels at an average speed of 30 m/s for .8 h. Find the total distance traveled in km.
For (1), consider this as a starter. A car travels due east for 30 miles, then turns due north and travels for another 40 miles. What is the distance? What is the displacement?
I won't say which one, but the distance and displacement form a right triangle: one of them makes up the two "legs" and the other the hypotenuse.
See how far that gets you.
For (3), consider these values. The car starts off at 0 mph, accelerates up to 65 mph and travels that speed for an hour, then comes to a town and must slow down to 25 mph for 10 minutes, then it comes to a stop. Without doing math, you should be able to tell is the maximum speed traveled at any instance could be greater than the average speed for the trip.
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To answer the question "Can the size of an object's displacement be greater than the distance the object travels?" we need to understand the definitions of distance and displacement.
Distance is a scalar quantity that refers to the total path length covered by an object. It only considers the magnitude of the motion and can never be negative.
Displacement, on the other hand, is a vector quantity that refers to the change in position of an object. It considers both the magnitude and direction of the motion and can be positive, negative, or zero.
So, to answer the question directly, it is possible for the size of an object's displacement to be greater than the distance the object travels. This occurs when the object changes direction during its motion, resulting in a shorter distance traveled but a larger displacement.
Moving on to the motion represented by a horizontal line on a distance-time graph. When a distance-time graph shows a straight horizontal line, it means that the object is not changing its position over time. In other words, it has a constant speed or is at rest. This type of motion is referred to as uniform motion.
Now, let's address the question of whether a car's instantaneous speed can ever be greater than its average speed during a trip. Instantaneous speed refers to the speed of an object at a particular moment or instant. Average speed, on the other hand, is the total distance traveled divided by the total time taken.
In general, it is possible for a car's instantaneous speed to be greater than its average speed at any given time during a trip. This can happen if the car goes through moments of high-speed acceleration or if the car stops or slows down for a significant period of time during the trip. However, over the entire trip, the average speed will still represent the overall average of the car's speed throughout the journey.
Regarding the scenario where you are walking towards the back of a bus that is moving forward with a constant velocity, your motion relative to the bus would be that you are moving in the opposite direction to the bus. Relative to a point on the ground, your motion would be a combination of your own walking motion and the velocity of the bus. If the bus is moving with a constant velocity, and you are walking at a constant speed towards the back of the bus, your motion relative to the ground would be the combination of the bus's velocity and your walking velocity.
Lastly, to find the total distance traveled in kilometers when a car travels at an average speed of 30 m/s for 0.8 hours, we can use the formula:
Distance = Speed x Time
First, let's convert the time from hours to seconds:
0.8 hours = 0.8 x 60 x 60 seconds = 2880 seconds
Then, we can calculate the distance:
Distance = 30 m/s x 2880 s = 86,400 meters
To convert the distance from meters to kilometers, we divide by 1000:
86,400 meters / 1000 = 86.4 kilometers
Therefore, the total distance traveled is 86.4 kilometers.