a train moves along a straight line. its location at time t is given by ( s(t)=\frac{50}{t} ), ( 1 leq t leq…

a train moves along a straight line. its location at time t is given by ( s(t)=\frac{50}{t} ), ( 1 leq t leq 9 ), where t is measured in hours and ( s(t) ) is measured in kilometers. complete parts (a) - (c) below. (c) use calculus to find the instantaneous velocity of the train at ( t = 2 ). the instantaneous velocity at ( t = 2 ) is (round to the nearest tenth as needed.)

a train moves along a straight line. its location at time t is given by ( s(t)=\frac{50}{t} ), ( 1 leq t leq 9 ), where t is measured in hours and ( s(t) ) is measured in kilometers. complete parts (a) - (c) below. (c) use calculus to find the instantaneous velocity of the train at ( t = 2 ). the instantaneous velocity at ( t = 2 ) is (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Recall the formula for instantaneous velocity

The instantaneous velocity (v(t)) is the derivative of the position function (s(t)). Given (s(t)=\frac{50}{t}=50t^{- 1}). Using the power rule ((x^{n})^\prime=nx^{n - 1}), the derivative (s^\prime(t)=v(t)=50\times(-1)t^{-1 - 1}).

Step2: Calculate the derivative

(v(t)=-\frac{50}{t^{2}})

Step3: Substitute (t = 2) into the velocity function

When (t = 2), (v(2)=-\frac{50}{2^{2}}=-\frac{50}{4}=- 12.5)

Answer:

(-12.5)