The velocity of a car after t seconds is 20 – 2t feet per second. How many seconds does it take for the car to come to a stop (velocity = 0)?

Question

b) How far does the car travel while coming to a stop?

c) How many seconds does it take the car to travel half the distance in part (b)?

My theory right now is that time is equal to 10 seconds for the 1st part of the question.

I am also thinking that the distance traveled is 10 ft.

I don't have any sources to check my answers, so any help is much appreciated.

Answer 1

a) 20-2t=0 --> t = 10 seconds

b) distance, s = ∫₀¹⁰v(t)dt = ∫₀¹⁰ 20-2t dt = 20t-t² |₀¹⁰ = 200-100 = 100 feet

c) 100/2 = 50

s(t) = 20t-t²

50 = 20t-t²

-t²+20t-50 = 0

By quadratic formula

t = 2.929, 17.0711 seconds

Pick 2.929 seconds because it is less than 10.

Answer 2

a) 10

b) 100 ft

c) SQRT(50) + 10