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dangina [55]
3 years ago
10

A driver with a 0.80-s reaction time applies the brakes, causing the car to have acceleration opposite the direction of motion.

Assume the acceleration is equal to -7.0 m/s^2. a. If the car is initially traveling at 26 m/s, how far does the car travel during the reaction time?
b. How far does the car travel after the brakes are applied and while skidding to a stop?
Physics
1 answer:
jeka943 years ago
4 0

Answer:

a) During the reaction time, the car travels 21 m

b) After applying the brake, the car travels 48 m before coming to stop

Explanation:

The equation for the position of a straight movement with variable speed is as follows:

x = x0 + v0 t + 1/2 a t²

where

x: position at time t

v0: initial speed

a: acceleration

t: time

When the speed is constant (as before applying the brake), the equation would be:

x = x0 + v t

a)Before applying the brake, the car travels at constant speed. In 0.80 s the car will travel:

x = 0m + 26 m/s * 0.80 s = <u>21 m  </u>

b) After applying the brake, the car has an acceleration of -7.0 m/s². Using the equation for velocity, we can calculate how much time it takes the car to stop (v = 0):

v = v0 + a* t

0 = 26 m/s + (-7.0 m/s²) * t

-26 m/s / - 7.0 m/s² = t

t = 3.7 s

With this time, we can calculate how far the car traveled during the deacceleration.

x = x0 +v0 t + 1/2 a t²

x = 0m + 26 m/s * 3.7 s - 1/2 * 7.0m/s² * (3.7 s)² = <u>48 m</u>

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s = ut + 1 / 2 at²

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Vertically,

s = 15.4 m

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15.4 = 0 + ( 1 / 2 * 9.8 * t² )

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s = 5.34 m

Therefore, the distance travelled by the ball before hitting the ground is 5.34 m

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