Rocket-powered sleds are used to test the responses of humans to acceleration. Starting from rest, one sled can reach a speed of 444 m/s in 1.80 s and can be brought to a stop again in 2.15 s.

(a) Calculate the acceleration of the sled when starting, and compare it to the magnitude of the acceleration due to gravity, 9.80 m/s2.
(b) Find the acceleration of the sled as it is braking and compare it to the magnitude of the acceleration due to gravity.

To calculate the acceleration of the sled when starting, we can use the formula:

acceleration = change in velocity / time taken

(a) Calculating the acceleration when starting:
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 444 m/s
Time taken (t) = 1.80 s

Using the formula, we have:
acceleration = (v - u) / t
acceleration = (444 m/s - 0 m/s) / 1.80 s
acceleration = 246.7 m/s^2

The acceleration of the sled when starting is 246.7 m/s^2.

Comparing it to the magnitude of the acceleration due to gravity, 9.80 m/s^2, we can see that the acceleration of the sled is significantly higher. This implies that the sled experiences much greater acceleration than the acceleration due to gravity during its start.

(b) Calculating the acceleration when braking:
Given:
Initial velocity (u) = 444 m/s
Final velocity (v) = 0 m/s (brought to a stop)
Time taken (t) = 2.15 s

Using the same formula, we have:
acceleration = (v - u) / t
acceleration = (0 m/s - 444 m/s) / 2.15 s
acceleration = -206.5 m/s^2

The acceleration of the sled when braking is -206.5 m/s^2, where the negative sign indicates deceleration.

Comparing it to the magnitude of the acceleration due to gravity, 9.80 m/s^2, we can see that the acceleration of the sled during braking is significantly higher in magnitude. This implies that the sled experiences much greater deceleration than the acceleration due to gravity during braking.

247 m/s^2