A car is driving north with an initial speed v0. We will describe this in terms of a coordinate system with positive y-axis pointing north and positive x-axis pointing east. At t=0 the driver sees a red-light and begins to slow down with an acceleration a(t)=−At (where A is a positive constant) which brings the car to rest just as it reaches the red-light. The driver then immediately begins to accelerate east at a constant rate with a(t)=B . a) Using the coordinate system specified, write down the initial velocity vector v(0) . Hint: Do not overthink this part. You should not be integrating anything just yet, we are simply asking you to write down a vector describing the initial velocity (north at speed v0). b) Determine the amount of time that elapses between the time when the car starts to slow down and when it comes to rest at the stoplight. You should express your answer in terms of v0, A and B. Hint: You may not need all of these quantities. c) Now determine the total amount of time that elapses between the time when the car starts to slow down and when it again reaches a speed of v0. You should express your answer in terms of v0, A and B.
A car is driving north with an initial speed v0. We will describe this in terms of a coordinate system with positive y-axis pointing north and positive x-axis pointing east. At t=0 the driver sees a red-light and begins to slow down with an acceleration a(t)=−At (where A is a positive constant) which brings the car to rest just as it reaches the red-light. The driver then immediately begins to accelerate east at a constant rate with a(t)=B .
a) Using the coordinate system specified, write down the initial velocity vector v(0) . Hint: Do not overthink this part. You should not be integrating anything just yet, we are simply asking you to write down a vector describing the initial velocity (north at speed v0).
b) Determine the amount of time that elapses between the time when the car starts to slow down and when it comes to rest at the stoplight. You should express your answer in terms of v0, A and B. Hint: You may not need all of these quantities.
c) Now determine the total amount of time that elapses between the time when the car starts to slow down and when it again reaches a speed of v0. You should express your answer in terms of v0, A and B.
d) Determine the magnitude of the average acceleration of the car from the time when it starts to slow down until it again reaches a speed of v0. You should express your answer in terms of v0, A and B. Hint: Before starting your calculations, you should consider both methods for finding the average acceleration, because one of them is notably easier than the other.
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