Acceleration Practice Quiz

Explanation
The cyclist's velocity changes from 1 m/s to 6 m/s over a time of 5 seconds. To find the average acceleration, we can use the formula: average acceleration = (change in velocity) / (time taken). The change in velocity is 6 m/s - 1 m/s = 5 m/s. The time taken is 5 seconds. Therefore, the average acceleration is 5 m/s / 5 s = 1 s^-2.

Explanation
The acceleration of the car can be calculated using the formula: acceleration = (final velocity - initial velocity) / time. In this case, the final velocity is 14 m/s, the initial velocity is 0 m/s, and the time is 2 seconds. Plugging these values into the formula, we get: acceleration = (14 m/s - 0 m/s) / 2 seconds = 14 m/s / 2 seconds = 7 m/s^2. Therefore, the correct answer is 7 s^-2.

Explanation
The acceleration of the bicycle rider can be calculated using the formula: acceleration = (final velocity - initial velocity) / time. In this case, the final velocity is 15 m/s, the initial velocity is 5 m/s, and the time is 10 seconds. Plugging these values into the formula, we get: acceleration = (15 m/s - 5 m/s) / 10 s = 10 m/s / 10 s = 1 m/s². Therefore, the acceleration is 1 s -2.

Explanation
The plane's acceleration can be calculated using the formula a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time taken. In this case, the plane starts from rest (vi = 0 m/s) and reaches a velocity of 75 m/s in 5 seconds (t = 5 s). Plugging in these values, we get a = (75 m/s - 0 m/s) / 5 s = 15 m/s^2. Therefore, the plane's acceleration is 15 s^-2.

Explanation
The car's velocity increased by 22 m/s in 11 seconds. To find the acceleration, we can use the formula: acceleration = change in velocity / time. Therefore, the acceleration is 22 m/s divided by 11 seconds, which equals 2 m/s^2.

Explanation
Since R cycles a third as quickly as Q, it means that Q cycles three times faster than R. Since R finished the race in 45 minutes, it means that Q would take 45/3 = 15 minutes to finish the race. Therefore, when P crossed the finish line, Q would be 15 minutes away from finishing the race. Since the race took 45 minutes in total, 15 minutes away from finishing would be 1/3 of the race distance. Therefore, Q would be 1/3 * 4500 = 1500 meters away from the finish line.

Explanation
The boy arrives at school 30 minutes earlier than usual when he speeds up to 9/5 of his previous speed. This means that the time he saves by speeding up is equal to 30 minutes. To find out how long he typically takes, we need to subtract the time saved (30 minutes) from the time it takes when he speeds up. Since he arrives at school 30 minutes earlier when he speeds up, the typical time he takes is 30 minutes longer than the time it takes when he speeds up. Therefore, the typical time he takes is 30 minutes + the time it takes when he speeds up, which is 30 minutes + 67.50 minutes = 97.50 minutes. However, none of the given answer choices match this value, so the question may be incomplete or not readable.

Explanation
The car's actual speed can be determined by dividing the distance traveled by the time taken. In this case, the car traveled 42 kilometers in 1 hour and 40.4 seconds. To convert the time to hours, we divide 40.4 seconds by 3600 (number of seconds in an hour), which gives us approximately 0.0112 hours. Dividing the distance of 42 kilometers by the time of 1.0112 hours, we get a speed of approximately 41.6 kilometers per hour. Since the car was traveling at 5/7ths of its maximum speed, we can calculate the maximum speed by dividing 41.6 by 5/7, which gives us approximately 59.43 kilometers per hour. Therefore, the car's actual speed is approximately 35 kilometers per hour.

Explanation
If the gradient of a graph is negative, it means that the graph is decreasing. In terms of acceleration, this indicates that the object is slowing down. Since the object is slowing down, the acceleration must be in the opposite direction of its motion. Therefore, the acceleration is positive.

Explanation
The car starts out at rest and reaches a speed of 18 m/s-1 in 6.0 seconds. To find the acceleration, we can use the formula: acceleration = (final velocity - initial velocity) / time. In this case, the initial velocity is 0 m/s and the final velocity is 18 m/s-1. Plugging these values into the formula, we get: acceleration = (18 m/s-1 - 0 m/s) / 6.0 s = 3 m/s-2. Therefore, the acceleration of the car is 3 m/s-2.