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You notice a stop sign 25 meters ahead causing you to hit the brakes. Your car’s deceleration is -4 m/s2 and it takes you 3.75 sec for your car to come to a stop. If you were originally speeding at 15 m/s before you brake, does your car stop before or after the stop sign? Draw the velocity-time graph for the car as it is braking.

Respuesta :

The distance the car travels before stopping is given by the initial velocity

of the car, the deceleration of the car.

The correct responses are;

  • First Part; The car stops after the stop sign

  • Second Part; The required velocity-time graph for the car as it is braking is attached.

Reasons:

The given information are;

Distance to the stop sign, D = 25 meters

Deceleration of the car, a = -4 m/s²

Time it takes the car to come to a stop, t = 3.75 sec

Initial speed of the car, u = 15 m/s

First part;

Required:

The distance it takes the car to stop.

Solution:

The distance, s, the car travels before stopping is given by the kinematic equation of motion Newton's law of motion as follows;

  • [tex]\displaystyle s = \mathbf{u \cdot t + \frac{1}{2} \cdot a \cdot t^2}[/tex]

Therefore;

[tex]\displaystyle s = 15 \times 3.75 + \frac{1}{2} \times (-4) \times 3.75^2 = \mathbf{28.125}[/tex]

The distance it takes the car to stop, s = 28.125 meters is longer than the distance to the stop sign, therefore;

  • The car stops after the stop sign

Second part;

The velocity of the car (as it is braking) is given by the formula;

v = u + a·t

Therefore, we have;

v = 15 - 4·t

  • Please find the required velocity-time graph of the car as it is braking, created with MS Excel

Learn more about kinematic equation of motion here:

https://brainly.com/question/24253179

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