Grant is an overzealous new driver, out for the first time without his mom. He stopped at a red lght on a country road-when the light turns green he takes off with an acceleration of 3.0 m/s^2. He manages to accelerate up to 30 m/s and travels at this top speed for three seconds before realizing he is approaching another red light. He immediatlely hits the brakes and slows to a stop in 7 seconds with constant acceleration.  A. What is the car's acceleration while he is slowing down? B. Draw qualitatively accurate position, velocity, and acceleration graphs for Grant's motion. Your graph axes should mimic those below  (one graph should be y axis as distance (x) and x axis time) (2nd graph should be y axis velocity and x-axis time) 3rd graph should be y axis acceleration and x axis time) C. What is the total distance that Grant travels between the two stop lights?

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Chapter3: Motion Along A Straight Line
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Grant is an overzealous new driver, out for the first time without his mom. He stopped at a red lght on a country road-when the light turns green he takes off with an acceleration of 3.0 m/s^2. He manages to accelerate up to 30 m/s and travels at this top speed for three seconds before realizing he is approaching another red light. He immediatlely hits the brakes and slows to a stop in 7 seconds with constant acceleration. 

A. What is the car's acceleration while he is slowing down?

B. Draw qualitatively accurate position, velocity, and acceleration graphs for Grant's motion. Your graph axes should mimic those below

 (one graph should be y axis as distance (x) and x axis time)

(2nd graph should be y axis velocity and x-axis time)

3rd graph should be y axis acceleration and x axis time)

C. What is the total distance that Grant travels between the two stop lights?

Expert Solution
Given data:

At t = 0 s, when Grant takes off at the Green light;

The velocity, v0=0 m/s

The acceleration, a1=3.0 m/s2

The final speed at this acceleration, v1=30 m/s which remains constant for t1 = 3 s

The final speed when Grant applies brakes for the second Red Light, v2=0 m/s after t2 = 7 s

 

 

 

Solution for (A):

The car's acceleration when it is slowing down can be determined by, 

a2=v2-v1t2

Substitute the values,

a2=0-30 m/s7 sa2=-4.2857-4.3 m/s2

The negative sign indicates that the speed of the car is decreasing.

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