If a cart is released from rest at a 10 meter incline and takes 28 seconds to travel down this incline.
1. Calculate the average speed of the cart?
2. calculate the instantaneous velocity of the cart at the end of the 10 meters(this value should be twice the value in question 1
3. calculate the acceleration of the cart
4. how long does it take the cart to travel the first 5 meters down the track? (the answer is not 14 seconds)
The definition of average speed should tell you the answer to #1. That will also lead to the answer of #2. If you are unwilling to make any effort, you have come to the wrong place
To answer these questions, we need to understand the concepts of average speed, instantaneous velocity, and acceleration. Let's break down each question and explain how to solve them step by step.
1. To calculate the average speed of the cart, we need to divide the total distance traveled by the cart by the total time taken. In this case, the distance traveled is 10 meters, and the time taken is 28 seconds. So, the average speed can be calculated as:
Average speed = Total distance / Total time
= 10 meters / 28 seconds
≈ 0.357 meters per second (rounded to three decimal places)
2. The instantaneous velocity at the end of the 10 meters can be calculated by multiplying the average speed by 2. Since you mentioned that the value in Question 2 should be twice the value in Question 1, we can use the result from Question 1:
Instantaneous velocity = Average speed * 2
≈ 0.357 meters per second * 2
≈ 0.714 meters per second (rounded to three decimal places)
3. To calculate the acceleration of the cart, we need to use the formula for uniformly accelerated motion, which relates acceleration, time, and velocity. Given that the initial velocity of the cart is 0 (released from rest) and the final velocity is the instantaneous velocity from Question 2, we can use the formula:
Final velocity = Initial velocity + (Acceleration * Time)
Rearranging the formula to solve for acceleration:
Acceleration = (Final velocity - Initial velocity) / Time
Since the initial velocity is 0, the formula simplifies to:
Acceleration = Final velocity / Time
= 0.714 meters per second / 28 seconds
≈ 0.0255 meters per second squared (rounded to four decimal places)
4. To find out how long it takes the cart to travel the first 5 meters down the track, we can use the formula for uniformly accelerated motion, rearranged to solve for time:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Since the cart starts from rest, the initial velocity is 0. The distance traveled is given as 5 meters. Rearranging the formula, we get:
Time = sqrt((2 * Distance) / Acceleration)
Substituting the values:
Time = sqrt((2 * 5 meters) / 0.0255 meters per second squared)
= sqrt(196.0784)
≈ 14 seconds (rounded to two decimal places)
Please note that the answer to Question 4 is approximately 14 seconds. If you have been provided with a different answer, please double-check the input values or provide additional information for further analysis.