- #1

fmiren

- 13

- 1

- Homework Statement
- I don't understand the limits of the definite integral in the acceleration problem below.

- Relevant Equations
- Acceleration and velocity equations

At time t=0 , a car moving along the + x -axis passes through x=0 with a constant velocity of magnitude v0 . At some time later, t

a(t)= 0 0≤t≤t

-c(t−t1) t

where c is a positive constants in SI units, and t

To get the velocity I integrate the accelaeration function and get v_0-c*(t_2-t_1)^2/2 since I think these should be the boundaries of the definite integral. Bu the correct answer is v_0-c*(t-t_1)^2/2 and they integrate from t (upper limit) to t1 (lower limit).

Could you please help me to understand it?

_{1}, it starts to slow down. The acceleration of the car as a function of time is given by:a(t)= 0 0≤t≤t

_{1}-c(t−t1) t

_{1}<t_{2}where c is a positive constants in SI units, and t

_{1}<t≤t_{2}is the given time interval for which the car is slowing down. Express your answer in terms of v_0 for v0 , t_1 for t1 , t_2 for t2 , and c as needed. What is v(t) , the velocity of the car as a function of time during the time interval t_{1}<t≤t_{2}?To get the velocity I integrate the accelaeration function and get v_0-c*(t_2-t_1)^2/2 since I think these should be the boundaries of the definite integral. Bu the correct answer is v_0-c*(t-t_1)^2/2 and they integrate from t (upper limit) to t1 (lower limit).

Could you please help me to understand it?

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