Velocity Timing

Question

Answer by filling in the blank below, then explain your answer.

Starting from rest, an automobile's velocity v (in ft/sec) is given by v = 180t / 2t + 10, where t is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of 

60 ft/sec (≈41 mph).

It will take ________ seconds for the car to reach a speed of 60 ft/sec.

Answer 1

60= 180t/(2t+10)

180t = 60(2t+10)

180t = 120t +600

180t-120t = 600

60t = 600

t = 600/60 = 10 seconds to reach 60 feet per second

Answer 2

We are given the velocity function and the final velocity, we just need to solve for how long it takes for the car to reach that velocity. We can set up a simple algabraic equation as follows:

60=180t / 2t+10 (Mulitply by 2t+10 on both sides)

60(2t+10) = 180t (Distribute)

120t + 600 = 180t (Subtract 120t on both sides)

600 = 60t

10 = t

after 10 seconds the car will reach 60 ft/sec