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)
Same question; same answer
To calculate the average speed of the cart, divide the total distance traveled by the total time taken. In this case, the total distance is 10 meters and the total time is 28 seconds.
1. Average speed = Total distance / Total time
Average speed = 10 meters / 28 seconds
Therefore, the average speed of the cart is approximately 0.36 meters per second.
To calculate the instantaneous velocity of the cart at the end of the 10 meters, we need to determine the final velocity. Since the initial velocity is zero (the cart is released from rest), the final velocity equals the average speed multiplied by 2.
2. Instantaneous velocity = 2 * Average speed
Instantaneous velocity = 2 * 0.36 meters per second
Therefore, the instantaneous velocity of the cart at the end of the 10 meters is approximately 0.72 meters per second.
To calculate the acceleration of the cart, we can use the formula:
Acceleration = Change in velocity / Time
Since the initial velocity is zero, the change in velocity is equal to the instantaneous velocity.
3. Acceleration = Instantaneous velocity / Time
Acceleration = 0.72 meters per second / 28 seconds
Therefore, the acceleration of the cart is approximately 0.026 meters per second squared.
To find out how long it takes the cart to travel the first 5 meters down the track, we need to calculate the time it takes to cover the whole 10 meters and then halve it.
4. Time taken to travel 5 meters = Total time / 2
Time taken to travel 5 meters = 28 seconds / 2
Therefore, it takes the cart approximately 14 seconds to travel the first 5 meters down the track.