Question

If you are running at 6m/s and deceleration at 2m/s^2,

a. Calculate the time it takes to stop.
b. Determine the final velocity.
c. Find the initial acceleration.
d. Assess the distance traveled during deceleration.

Answer 1

The time taken to stop is 3 seconds, the final velocity is 0 m/s, the initial acceleration (or deceleration) is -2 m/s², and the distance traveled during deceleration is 9 meters.

Step-by-step explanation:

To solve this physics problem, we address each part step-by-step:

1. Calculate the time it takes to stop: The formula for time t when decelerating from an initial velocity u to a final velocity v at a constant deceleration a is given by t = (v - u) / a. Since we want the time taken to stop completely, v = 0 m/s, and u = 6 m/s. Substituting these values and the given deceleration of a = -2 m/s2 (negative because it is a deceleration), we get t = (0 - 6) / (-2) = 3 seconds.
2. Determine the final velocity: Since we are calculating the time taken to come to a stop, the final velocity v is 0 m/s.
3. Find the initial acceleration: The initial acceleration is the initial rate of change of velocity of the runner, which is given as the deceleration rate of -2 m/s2.
4. Assess the distance traveled during deceleration: Using the formula s = ut + (1/2)at2, with u = 6 m/s, a = -2 m/s2 and t = 3 seconds, we calculate the distance s to be s = 6(3) + (1/2)(-2)(32) = 18 - 9 = 9 meters.