Scalars & Vectors in 1 Dimension
Is speed a scalar or vector quantity?
Scalar because it only has magnitude and no direction.
A car travels 200m in 10 seconds at a constant velocity. What is the car's velocity?
20m/s
What is the slope of a velocity vs time graph? What is the area under the curve of a velocity vs time graph?
Acceleration is the slope and displacement is the area.
A train is moving east at 20m/s. A person on the train walks to the front of the train at 1m/s relative to the train. What is the person's speed relative to the ground?
21m/s
How do you find the combined length of vectors if one points along the x-axis while the other points along the y-axis?
Pythagorean Theorem
A runner completes one lap around a 400m track. What is the runner's total displacement? What distance did the runner cover?
The displacement is 0m and the distance covered is 400m.
A bicycle moves at a constant velocity of 10m/s for 5 seconds. How far does it travel?
50m
A ball is thrown straight up in the air. What is its velocity at its highest point?
0m/s
When could the relative velocity between two objects be zero even if the objects are moving?
When two objects move at the same speed and in the same direction.
Vector A with a magnitude of 5 units, points along the positive x-axis while Vector B with a magnitude of 12 units, points along the positive y-axis. What is the magnitude of A + B?
13 units
What is the difference between average speed and instantaneous speed?
Average speed is the total distance traveled divided by the total time taken. Instantaneous speed is the speed at a specific moment in time.
How can an object have a positive velocity and a negative acceleration at the same time?
When an object is moving in the positive direction but slowing down.
What could be a situation where an object has a constant speed but a changing velocity?
Two cars approach an intersection. Car A is moving east at 20m/s while Car B is moving north at 30m/s. What is the velocity of Car A relative to Car B?
36.1m/s
How does increasing the angle of launch affect the range and maximum height of a projectile if the initial speed remains constant?
The ranges increases until 45 degrees and maximum height continually increases until 90 degrees.
A train travels at a constant velocity of 30m/s for 20 seconds, then it decelerates at a rate of 2m/s2 for 5 seconds. How far did the train travel in total?
725m
A ball is thrown at an angle of 30 degrees above the horizontal with a initial velocity of 15m/s. Calculate the horizontal displacement of the ball. (g=10s)
19.49m
A cyclist travels 120m in 12 seconds. For the first 4 seconds, the acceleration is 2m/s2. What is the speed at the end of the first 4 seconds?
8m/s
A plane needs to fly north, however there is a wind blowing from the west at 35m/s. If the planes speed in the air is 250m/s, what will be the planes speed on the ground?
247.5m/s
A projectile is launched with initial velocity of v at and angle (-) with the horizontal. Find the range of the projectile on level ground.
(v2(sin(2(-)))/ g
A projectile is launched vertically upwards. Air resistance is not negligible. How does air resistance affect the maximum height reached by the projectile?
Air resistance reduces the maximum height of the projectile.
t/sqrt(2)
What should a velocity vs time graph look like for an object that starts from rest, has a constant acceleration to a certain speed, maintains the speed for while, and then decelerates to a stop?
A straight line starting from zero should go diagonally upwards before becoming a horizontal line, and then sloping diagonally downward before stopping at zero.
There are two cars A and B which are approaching each other on a straight road. Car A travels at 30m/s and Car B travels at 20m/s. When they are 100m apart, both drivers apply their breaks. If Car A decelerates at 2m/s2 and Car B decelerates at 3m/s2, will the cars collide?
Yes they will.
A river flows east at 1.5m/s. A boat crosses the river with a velocity of 2.5m/s relative to the water, heading 30 degrees northwest. What is the velocity of the boat relative to the shore?
2.18m/s