How Much Do You Know About Acceleration?

The term "acceleration" refers to any change in the velocity of an object, which can include speeding up, slowing down, or changing direction. Therefore, the correct answer is "All of the above" because all of these options are examples of acceleration.

Centripetal acceleration occurs because an object is changing direction. When an object moves in a circular path, it constantly changes its direction, even if its speed remains constant. Centripetal acceleration is the acceleration directed towards the center of the circle, which keeps the object moving in a curved path. This acceleration is necessary to counteract the tendency of the object to move in a straight line and ensures that it stays on its circular path.

When a change in velocity is negative, it means that the object is slowing down. Negative velocity indicates that the object is moving in the opposite direction of its initial motion or is decelerating. This means that the object's speed is decreasing over time.

The velocity-time graph shows a straight line with a negative slope, indicating that Peter's velocity is decreasing over time. Since velocity is a measure of both speed and direction, this means that Peter's speed is decreasing as he runs in a constant direction on the straight road.

When velocity changes the same amount over each time interval, it means that the rate of change of velocity is constant. This indicates that the object is experiencing a constant acceleration. Therefore, the correct answer is constant.

The value of acceleration on a velocity-time graph is shown by the slope of the line. The slope represents the rate at which velocity is changing over time. A steeper slope indicates a greater change in velocity, indicating a higher acceleration. Conversely, a flatter slope indicates a smaller change in velocity, indicating a lower acceleration. Therefore, the slope of the line on a velocity-time graph directly represents the value of acceleration.

The average acceleration of a car can be calculated by dividing the change in velocity by the time taken. In this case, the car goes from 0 m/s to 25 m/s in 8.0 s. The change in velocity is 25 m/s - 0 m/s = 25 m/s. Dividing this by the time taken, we get 25 m/s / 8.0 s = 3.1 m/s^2. Therefore, the correct answer is 3.1 m/s^2.

During uniform circular motion, the speed of the object remains constant. This is because the object is moving in a circle at a constant rate, meaning it covers the same distance in the same amount of time. However, the velocity of the object is not constant because velocity includes both speed and direction. In circular motion, the direction of the object is constantly changing as it moves around the circle, even though its speed remains the same. Displacement is also not constant as it depends on the starting and ending positions of the object.

The cheetah's acceleration is given as 6.0 m/s^2. To find the time it takes for the cheetah to speed up from 10.5 m/s to 12.2 m/s, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the formula to solve for time, we have t = (v - u) / a. Plugging in the values, we get t = (12.2 - 10.5) / 6.0 = 1.7 / 6.0 = 0.28 s.

The cyclist starts with an initial speed of 10.0 m/s and accelerates at a rate of 0.500 m/s^2. To find the final speed after 9.0 s, we can use the equation: final speed = initial speed + (acceleration * time). Plugging in the values, we get: final speed = 10.0 m/s + (0.500 m/s^2 * 9.0 s) = 10.0 m/s + 4.5 m/s = 14.5 m/s. Therefore, the correct answer is 14.5 m/s.