Final answer:
To reach a speed of 2.00 m/s with an acceleration of 1.40 m/s², it takes the commuter 1.43 seconds. The commuter's deceleration when she brakes to a stop in 0.800 seconds is -2.50 m/s². Therefore, the correct answer is option a) (a) 1.43 s, (b) -2.50 m/s²
Step-by-step explanation:
To determine how long it takes for a commuter to reach a speed of 2.00 m/s with an acceleration of 1.40 m/s², we use the equation for constant acceleration, v = at, where v is the final velocity, a is the acceleration, and t is the time. Solving for time, we get t = v/a, which gives us t = 2.00 m/s / 1.40 m/s² = 1.43 s.
For part (b), if she brakes to a stop in 0.800 s, the deceleration can be found using the formula a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. Since she comes to a stop, the change in velocity is -2.00 m/s (the negative sign indicates a decrease in speed), and Δt is 0.800 s. Thus, her deceleration is a = -2.00 m/s / 0.800 s = -2.50 m/s², where the negative sign indicates a deceleration.
(a) To find the time it takes for the car to reach a speed of 2.00 m/s, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation to solve for t, we have t = (v - u) / a. Plugging in the given values, we get t = (2.00 m/s - 0 m/s) / 1.40 m/s² = 1.43 s.
(b) To find the deceleration when the car brakes to a stop, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, and a is the deceleration. Rearranging the equation to solve for a, we have a = (v - u) / t. Plugging in the given values, we get a = (0 m/s - 2.00 m/s) / 0.800 s = -2.50 m/s².
Therefore, the correct answer is option a) (a) 1.43 s, (b) -2.50 m/s²