Final answer:
A car going at 35 m/s with an acceleration of -5 m/s² takes 7 seconds to stop. During this time, the car travels a distance of 122.5 meters while braking.
Step-by-step explanation:
To calculate how long a car takes to stop when braking with an acceleration of -5 m/s², we can use the formula for acceleration: a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time. We know the car is initially going at 35 m/s and comes to a stop (vf = 0), and the acceleration is given as -5 m/s². Using these values:
-5 m/s² = (0 m/s - 35 m/s) / t
-5 m/s² = -35 m/s / t
t = 35 m/s / 5 m/s² = 7 seconds
The car takes 7 seconds to stop. To find the distance the car travels while braking, we can use the formula for distance under constant acceleration: d = vi*t + (1/2)*a*t². Plugging in the values:
d = 35 m/s * 7 s + (1/2) * (-5 m/s²) * (7 s)²
d = 245 m - (1/2) * 5 m/s² * 49 s²
d = 245 m - 122.5 m
d = 122.5 meters
The car goes 122.5 meters while braking.