The velocity of a particle moving along a straight line is given by v(t)=6t2+4t−5 cm/sec at time t seconds with initial position s(0)=3 cm. What is the position of the particle at t=2 seconds, in cm?

s(2) = 17 cm

Step-by-step explanation:

We are told that the velocity function is;

v(t) = 6t² + 4t − 5 cm/sec

Integral of velocity gives distance.

Thus;

s(t) = ∫v(t) = ∫6t² + 4t − 5

s(t) = 2t³ + 2t² - 5t + c

We are told that s(0)=3 cm

Thus;

s(0) = 2(0)³ + 2(0)² - 5(0) + c = 3

Thus; c = 3

Thus;

s(t) = 2t³ + 2t² - 5t + 3

At t = 2 secs

s(2) = 2(2)³ + 2(2)² - 5(2) + 3

s(2) = 17 cm

Find the cost of the first 10 hours:

10 hours = $220 x 10
10 hours = $2200


Find the cost of the next 5 hours (only the second mechanic worked):

5 hours  = $2725 - $2200 
5 hours = $525


Hourly charge of the second mechanic:

5 hours = $525
1 hour = $525 ÷ 5
1 hour = $105


Hourly charge of the first mechanic:

$220 - $105 = $115


First mechanic = $115/hour ; Second mechanic = $105/hour