Physics Quiz: Motion With Constant Acceleration

Explanation
The bike consistently gains speed from zero to ten meters per second over a span of 25 meters. To calculate the bike's acceleration, we can use the formula for acceleration: acceleration = change in velocity / time. In this case, the change in velocity is 10 m/s (final velocity) - 0 m/s (initial velocity), which is 10 m/s. The time taken to achieve this change in velocity is 25 meters. Therefore, the acceleration is 10 m/s / 25 m = 0.4 m/s2. However, none of the given options match this calculation. Therefore, the correct answer is not available.

Explanation
The SI unit of distance is meter. The meter is defined as the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second. It is the most commonly used unit for measuring distances and is widely used in scientific and everyday applications. The kilometer is a larger unit of distance, equal to 1000 meters, while Newton is the unit of force and second is the unit of time.

Explanation
Acceleration is the correct answer because it refers to the rate of change of velocity. In other words, acceleration measures how quickly an object's velocity is changing over time. If an object is accelerating, its velocity is either increasing or decreasing. Speed, on the other hand, only measures how fast an object is moving without considering the direction or change in velocity. Displacement refers to the change in position of an object, while momentum is the product of an object's mass and velocity.

Explanation
A vector is a quantity that has both direction and magnitude. It represents a physical quantity that requires both a numerical value and a specific direction to fully describe it. Examples of vectors include displacement, velocity, and force. Scalars, on the other hand, only have magnitude and do not have a specific direction associated with them. Examples of scalars include temperature, mass, and time. Therefore, the correct answer is vector.

Explanation
A horizontal line on a graph of distance vs time indicates that the object's speed is zero. This means that the object is not moving or its velocity is constant. When the distance does not change over time, it implies that the object is at rest or not in motion. Therefore, the speed of the object is zero.

Explanation
The plane starts with an initial speed of 70.0 m/s and decelerates at a rate of 1.50 m/s^2 for 10 seconds. To find the maximum speed, we need to determine the final velocity after deceleration. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the final velocity as follows: v = 70.0 m/s + (-1.50 m/s^2)(10 s) = 70.0 m/s - 15 m/s = 55 m/s. Therefore, the plane's maximum speed is 55 m/s.

Explanation
The particle's initial velocity is 4 m/s and its speed after 3 seconds is 14 m/s. This means that the particle has undergone an acceleration of (14 m/s - 4 m/s) / 3 s = 10 m/s^2. Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can solve for s. Plugging in the given values, we have (14 m/s)^2 = (4 m/s)^2 + 2(10 m/s^2)s. Simplifying this equation gives us s = 27 m. Therefore, the particle has moved 27 meters in that time frame.

Explanation
The rock experienced an acceleration of 10.0 m/s2. This can be determined using the equation of motion, which states that the final velocity squared is equal to the initial velocity squared plus two times the acceleration times the distance traveled. In this case, the initial velocity is 40.0 m/s, the final velocity is 0 m/s (since the rock hits the ground), and the distance traveled is 80.0 meters (the height of the cliff). By substituting these values into the equation and solving for acceleration, we get an acceleration of 10.0 m/s2.

Explanation
Displacement refers to the shortest possible path followed by an object. It is a vector quantity that represents the change in position of an object from its initial point to its final point. Unlike distance, which is a scalar quantity and refers to the total length traveled, displacement takes into account the direction of motion. Therefore, displacement is the correct answer in this case.

Explanation
In the scenario where an object starts from a complete stop and is subjected to constant acceleration, the velocity of the object at any moment can be calculated by adding the product of acceleration and time to the initial velocity. For example, if the object begins with no initial movement (zero velocity) and accelerates at a constant rate, after one second, its velocity will be equivalent to the acceleration value.
To illustrate, if an object has an acceleration of 5 meters per second squared, then after one second, its velocity becomes 5 meters per second. This happens because, in each second, the speed increases by the acceleration rate. So, simply put, after one second, the increase in velocity equals the rate of acceleration.