Question

A car is travelling at 72km/h and the brakes are fully applied, producing a constant deceleration of 12m/s^2.
a) Verify that the velocity function v(t)=-12t+20, where t = seconds, gives this deceleration and initial velocity.
b) How long does it take for the car to come to a complete stop?

Answer 1

so first convert 72km an hour to m/s

Answer 2

we get 20m/s

Answer 3

the car comes to a stop when its velocity is 0

Answer 4

-12t+20 = 0

Answer 5

solve for t

Answer 6

t would equal to 5/3? @TylerD

Answer 7

20/12 = 5/3 yes

Answer 8

to verify the velocity function, the derivative of it is -12, which is acceleration.

Answer 9

and because its in m/s^2, we had to convert the km/hr to m/s

Answer 10

you can also get the position function, by integrating.

p(t)=-6t^2+20t

Answer 11

but no need, just saying..

Answer 12

oh okay! thanks a lot! If you don't mind, can you explain what integrating? I'm curious

Answer 13

@TylerD you are thinking, good! but you have an error
you integrate the velocity to get the distance
same as differentiate the distance to get the velocity
@esam2 basically integration and differentiation are opposites like multiplication and division

Answer 14

when you differentiate you are finding the rate of change
in essence the slope as the change in the independent variable approaches zero

Answer 15

@TylerD sorry, I read the post without the period and you did not say what you were integrating. I thought you were integrating the Position function P(t).

don't forget your C when you integrate