A stationary boat accelerates to 90 km/hr over 1 km. What is the time it takes to do this?

Question

A stationary boat accelerates to 90 km/hr over 1 km. What is the time it takes to do this?

Ans: 80s

Answer 1

Hi Michael

 

 

Initial speed = 0

Final speed = 90 km/hr

Acceleration = Change in speed /time = 90/ time

 

Now distance moved = 1 km

 

Distance moved = 1/2 (acceleration) * time ²

 

1= 1/2 * (90/time)* time ²

 

1= 1/2 * 90 * time

Gives time = 2/90 = 1/45 hr=(60*60)/45 Sec= 80 sec

= 

 

Answer 2

This can also be done (assuming constant acceleration, as we always do in cases like this at this level) in one step -- well, one step plus a conversion -- using the kinematic expression:

 

d = (1/2)(v_o+v)t

 

You can even keep you d in km and v in km/hr, and get t in hours.

 

1 km = (1/2)(0 + 90 km/hr)t

 

1 = 45t

 

t = 1/45 = 0.022 hr  * (3600 s/1 hr) = 80 s