Answer to Question #101492 in Calculus for Joe

Question #101492
The car's speed after braking is v (t) = 16.9 - 0.1t2 (where time t is seconds).

a) How long does the braking last?

(b) the distance traveled by the first 3 and last 3 cars
within seconds of starting braking?

c) How long does the car move during the entire braking?
1
Expert's answer
2020-01-20T09:47:22-0500

a) The braking process occurs until the moment when the speed becomes equal to zero. Hence


"16.9-0.1t^2=0 \\implies t^2=169 \\implies t=13s"

b) We find the required distance using the formula


"d=\\smallint_0^{3}v(t)dt+\\smallint_{10}^{13}v(t)dt=\\smallint_0^{3}(16.9-0.1t^2)dt+\\smallint_{10}^{13}(16.9-0.1t^2)dt="

"=(16.9t-\\frac{0.1t^3}{3})_0^{3}+(16.9t-\\frac{0.1t^3}{3})_{10}^{13}=16.9\\times3-\\frac{0.1\\times{3^3}}{3}-0+"

"+16.9\\times13-\\frac{0.1\\times{13^3}}{3}-16.9\\times10+\\frac{0.1\\times{10^3}}{3}=60.6"


c) During braking, the car travels a distance equal to


"d=\\smallint_0^{13}v(t)dt=\\smallint_0^{13}(16.9-0.1t^2)dt=(16.9t-\\frac{0.1t^3}{3})_0^{13}""d=16.9\\times13-\\frac{0.1\\times{13^3}}{3}-0=146.47"

Answer. a) 13s. b) 60.6 c) 146.47.


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