I have velocity question about a boat & displacement Q. College Gen Physics?

Question

A speedboat starts from rest and accelerates at +2.01m/s^2 for 7.00s. At the end of this time, the boat continues for an additional 6.00s with an acceleration of +0.518m/s^2. Following this, the boat accelerates at -1.49m/s^2 for 8.00s. a) What is the velocity of the boat at t=21.0s. b) Find the total displacemnt of the boat.

Answer 1

This is a "piecewise linear" sequence of motion
from 0<=t<=7
v(7)=2.01*7
14.07 m/s

displacement (distance)=.5*2.01*7^2
=49.245 m

next
v(13)=14.07+0.518*6
=17.178 m/s

d(13)=49.245
+14.07*6+.5*0.518*36

=142.989

next
v(21)=17.178-1.49*8
5.258 m/s

d(21)=142.989+
17.178*8-.5*1.49*64

232.733 m (this is the total displacement)

j

Answer 2

it is assuming perfect situations ( vehicle oiled completely, air too skinny to oppose stream, etc.) it is clearly impossible, even inspite of the undeniable fact that it makes issues that plenty easier (no particularly, you have no longer any concept how plenty easier it makes issues, and that i do no longer the two, even inspite of the undeniable fact that it is plenty). Now, right this is the capture: we gained't pull power out of nowhere, and we gained't deliver it everywhere. via fact the vehicle isn't working, we are actually not getting power out of gas, and because we've not any air friction or area friction (perfect, bear in ideas?), the vehicle could have a fixed quantity of power all throughout the time of the technique. So, stream ability power (kinetic) and hight additionally ability power (in spite of each thing, lifting rocks is tiresome, and dropping them on some thing can harm it, precise?). additionally power(E) from hight is E=m*g*h, (m*g) is the vehicle's weight and (h) is the hill's height. Kinetic power is E=m*(v^2), the place (v) is the fee. Now, on account that power maintains to be consistent (perfect and stuff) the two E's are equivalent (at their optimal values, no longer all the way by way of. suitable for saved power, backside for velocity). which ability m*g*h=m*(v^2), as a result g*h=v^2. So, distance traveled and time taken do no longer count, you have the vehicle loose-fall from the hill's hight and nonetheless get the comparable velocity (basically downwards instead of forwards). notice that, right here interior the real international, it is doubtless distinctive than the single physics artwork with, the perfect state won't be able to be finished. via fact of this, the longer the descend, the greater power (and as a result velocity) you lose, and the tip velocity would be distinctive. yet do no longer stress your instructor too plenty with that, it is no longer their fault XD