a car moving at 25m/s undergoes an acceleration of -2.3m/s. calculate a) the time needed to stop this car and b) the distance the car will travel before stopping.
25 m/s / 2.3 m/s^2 = 10.87 s
distance = 25t - 1.15t^2 where t = 10.87
To calculate the time needed to stop the car, we can use the equation:
final velocity (Vf) = initial velocity (Vi) + acceleration (a) * time (t)
Given:
Initial velocity (Vi) = 25 m/s
Acceleration (a) = -2.3 m/s^2 (the negative sign indicates deceleration)
a) Calculating the time needed to stop the car:
To find the time needed to stop the car, we need to find the final velocity (Vf) when the car comes to a stop. In this case, the final velocity is 0 because the car has stopped.
0 = 25 m/s + (-2.3 m/s^2) * t
Rearranging the equation, we get:
2.3 m/s^2 * t = 25 m/s
t = 25 m/s / 2.3 m/s^2
t ≈ 10.87 s (rounded to 2 decimal places)
Therefore, it will take approximately 10.87 seconds to stop the car.
b) Calculating the distance the car will travel before stopping:
To find the distance the car will travel before stopping, we can use the formula:
distance (d) = initial velocity (Vi) * time (t) + (1/2) * acceleration (a) * time^2 (t^2)
d = 25 m/s * 10.87 s + (1/2) * (-2.3 m/s^2) * (10.87 s)^2
d = 272.175 m - 137.065 m
d ≈ 135.11 m (rounded to 2 decimal places)
Therefore, the car will travel approximately 135.11 meters before stopping.