The car is traveling at a speed of 60 mi/hr as it approaches point A. Beginning at A, the car decelerates at a constant 7ft/sec2 until it gets to point B, after which its constant rate of decrease of speed is 3ft/sec2 as it rounds the interchange ramp. Determine the magnitude of the total car acceleration (a) just before it gets to B, (b) just after it passes B, and (c) at point C.

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To determine the magnitude of the total car acceleration at different points, we need to consider both the initial speed and the rate of decrease in speed at each interval.

(a) Just before the car gets to point B:
The initial speed of the car is 60 mi/hr. To convert this to ft/sec, we multiply by the conversion factor 5280 ft/mi and 1/3600 hr/sec:
Initial speed = 60 mi/hr * 5280 ft/mi * 1/3600 hr/sec = 88 ft/sec

The car decelerates at a constant rate of 7 ft/sec^2. Since the direction of the acceleration is opposite to the initial velocity, the magnitude of acceleration is given by the rate of decrease in speed, which is equal to the magnitude of the deceleration:
Acceleration = -7 ft/sec^2

(b) Just after the car passes point B:
At point B, the car switches to a different rate of decrease in speed. The new rate is -3 ft/sec^2. The direction of the acceleration remains the same (opposite to the velocity), so the magnitude of the acceleration remains the same:
Acceleration = -3 ft/sec^2

(c) At point C:
We are not given any specific information about point C, so we cannot determine the magnitude of acceleration at that point.

To summarize:
(a) Just before point B: Acceleration = -7 ft/sec^2
(b) Just after passing point B: Acceleration = -3 ft/sec^2
(c) At point C: Not enough information given to determine the magnitude of acceleration.

To determine the magnitude of the car acceleration at different points, we need to understand the concept of acceleration. Acceleration is the rate at which an object's velocity changes over time.

(a) Just before the car gets to point B:
To find the magnitude of acceleration just before reaching point B, we need to calculate the deceleration rate. The car decelerates at a constant rate of 7 ft/sec². However, the given speed is in miles per hour (mi/hr), so we need to convert it to feet per second (ft/sec).

1 mile = 5280 feet
1 hour = 3600 seconds

The car's speed is 60 mi/hr, so:

Speed in ft/sec = (60 mi/hr) * (5280 ft/mi) / (3600 sec/hr)
Speed in ft/sec = 88 ft/sec

Now we know the initial speed before deceleration. The deceleration rate is given as 7 ft/sec². Since deceleration is just the opposite of acceleration but with a negative sign, the magnitude of the total acceleration just before reaching point B is the sum of the initial speed and the deceleration:

Magnitude of acceleration = Initial speed - Deceleration rate
Magnitude of acceleration = 88 ft/sec - 7 ft/sec² = 81 ft/sec²

So, the magnitude of the total car acceleration just before it gets to point B is 81 ft/sec².

(b) Just after the car passes point B:
At point B, the car's speed is decreasing at a constant rate of 3 ft/sec². The magnitude of the total acceleration just after passing point B can be calculated using the same approach as in part (a).

Magnitude of acceleration = Initial speed - Deceleration rate
Magnitude of acceleration = 0 ft/sec - 3 ft/sec² = -3 ft/sec²

Note: The negative sign indicates that the car's acceleration is in the opposite direction of its initial motion. In this case, it represents the deceleration.

So, the magnitude of the total car acceleration just after it passes point B is 3 ft/sec².

(c) At point C:
No specific information is given about the change in acceleration at point C. Therefore, we cannot determine the magnitude of the acceleration at that point without additional data.

I recommend you find another class, in this you are wasting your time.

a) 7ft/sec^2
b) 3ft/sec^2
c) There is no point C.

The name of the class "Dynamics of Rigid Bodies" sounds swanky, doesn't it. Much sound and fury, signifying nothing.