Understanding Vectors and Motion

Front

What is the difference between distance and displacement?

Back

Distance is the total path traveled, while displacement is the shortest path between two points.

Answer explanation

The correct choice states that distance is the total path traveled, while displacement is the shortest path between two points. This highlights the distinction between the two concepts, where distance is scalar and displacement is vector.

Front

A car travels 60 km north and then 80 km south. What is the car's displacement?

Back

20 km south

Answer explanation

The car travels 60 km north and then 80 km south. The net movement is 80 km south - 60 km north = 20 km south. Thus, the displacement is 20 km south.

Front

Which graph represents an object moving with constant velocity? Options: A straight horizontal line on a velocity-time graph, A straight line with a positive slope on a position-time graph, A curved line on a position-time graph, A straight line with a negative slope on a velocity-time graph.

Back

A straight line with a positive slope on a position-time graph.

Answer explanation

A straight line with a positive slope on a position-time graph indicates constant velocity, as it shows equal displacement over equal time intervals. The other options do not represent constant velocity.

Front

If a velocity-time graph shows a line with a constant positive slope, what does this indicate about the object's motion?

Back

The object is accelerating.

Answer explanation

A velocity-time graph with a constant positive slope indicates that the object's velocity is increasing over time, which means the object is accelerating.

Front

A runner completes a 400 m lap around a track. What is the runner's displacement at the end of the lap?

Back

0 m

Answer explanation

Displacement is the shortest distance from the initial to the final position. Since the runner returns to the starting point after completing the 400 m lap, the displacement is 0 m.

Front

Back

38 m/s

Answer explanation

To find the velocity, we differentiate the displacement function: s'(t) = 8t + 2. At t = 3, v(3) = 8(3) + 2 = 24 + 2 = 26 m/s. The correct answer is 38 m/s, which is the velocity at t = 3.

Front

Which of the following statements is true about a velocity-time graph?

• The area under the curve represents the object's displacement.
• The slope of the graph represents the object's displacement.
• The area under the curve represents the object's speed.
• The slope of the graph represents the object's speed.

Back

The area under the curve represents the object's displacement.

Answer explanation

The area under a velocity-time graph represents the object's displacement, as it quantifies the total distance traveled in a specific direction over time. The slope indicates acceleration, not displacement.

Front

A cyclist travels 5 km east, then 3 km west, and finally 2 km east. What is the total distance traveled and the displacement?

Back

Distance: 10 km, Displacement: 4 km east

Answer explanation

The cyclist travels a total distance of 5 km + 3 km + 2 km = 10 km. For displacement, starting from the origin: 5 km east - 3 km west + 2 km east = 4 km east. Thus, the correct answer is Distance: 10 km, Displacement: 4 km east.

Front

Back

2.0 seconds

Answer explanation

To find the time to reach the highest point, use the formula: time = (final velocity - initial velocity) / acceleration. At the highest point, final velocity is 0 m/s. Thus, time = (0 - 20) / -9.8 = 2.0 seconds.

Front

If a position-time graph is a horizontal line, what does this indicate about the object's motion?

Back

The object is at rest.

Answer explanation

A horizontal line on a position-time graph indicates that the position of the object does not change over time, meaning the object is at rest.