Let's consider a more realistic version of problem 1. Again, at time t = 0 the...

 

Transcribed Image Text:

Let's consider a more realistic version of problem 1. Again, at time t = 0 the car is at rest at position x = 0, but this time assume that the acceleration is given by the equation a = a[1 exp(-t/T)], where exp(x) = ex. In other words, the acceleration takes some time (depending on the value of the "time constant" T) to increase from its initial value of a = 0 to its final value a. (a) Perform the appropriate integral to get an expression for v(t), the velocity at any time t 0. Write your answer in terms of the variables ap, T, and t only. Let's consider a more realistic version of problem 1. Again, at time t = 0 the car is at rest at position x = 0, but this time assume that the acceleration is given by the equation a = a[1 exp(-t/T)], where exp(x) = ex. In other words, the acceleration takes some time (depending on the value of the "time constant" T) to increase from its initial value of a = 0 to its final value a. (a) Perform the appropriate integral to get an expression for v(t), the velocity at any time t 0. Write your answer in terms of the variables ap, T, and t only.