A Porsche challenges a Honda to a 400 m race.Because the Porsche’s acceleration of 3.5 m/s² is larger than the Honda’s 3.0 m/s², the Honda gets a 50 m head start.Both cars start accelerating at the same instant. Who wins?
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Time taken by honda to complete race =
D = 1/2 a*t*t
350*2/3 =t*t
t =15.2752 sec.
Time taken by porsche to complete race=
D = 1/2 A*T*T
400*2/3.5 =T*T
T=15.11Sec.
As time taken by porsche is less than time taken by honda;
Hence porsche Wins!!!
Use the basic Law of motion,
S = ut + 1/2 * at^2
S=distance=400 m for porsche and =350 m for honda
u=initial velocity =0
so for porsche
S1=400 = 1/2 * 3.5 * t^2 —–> t = 15.11 s
for honda
S2=350 = 1/2 * 3 * t^2 —–> t = 15.27 s
So the porshe wins
ok so the honda has acc of 3 m/s/s, and the porsche has 3.5m/s/s. the honda only needs to cover 350m. now, all you have to do is use simple motion equations to get the time for both cars, and whichever is less will be the winner.
for the honda:
s= ut + 0.5at^2
350 = 0 + 0.5 x 3t^2
350/1.5 = t^2
233.33 = t^2
t = 15.28 seconds
for the porsche:
s = ut + 0.5at^2
400 = 0 + 0.5 x 3.5t^2
400/1.75 = t^2
t = 15.11 seconds
therefore, the porsche will overtake the honda somewhere near the end to win by 0.17 seconds, in a time of 15.11 seconds.
You can solve this using the kinematic equation X = VoT + 1/2 A T^2
For the Porsche, the total displacement for his vehicle is X = 450m and A = 3.5 m/s^2. Initial velocity is Vo = 0m/s. Solve for time T.
For the Honda, the total displacement is only X = 400m and A = 3.0 m/s^2. Initial velocity is also Vo = 0 m/s. Solve for time T.
Whoever has the lower time value crosses the finish line first.
Honda will win at 400m race. The time for honda to reach the destination is lesser than porsche.
I used x=1/2at^2 and just subsituted the information in the equation. The porsche will go 400 meters in 7.55928 secs and the honda will go 350 meters in 7.6376 meters so the porche wins.
X = distance
1/2 constant
a= acceleration
t^2= the time
I don’t see why I would be wrong
Porsche wins. Look how:-
We have, s = ut +1/2at^2
both have u = 0, so, s = 1/2 at^2
2s/a = t^2
Now, For Porsche
t^2 = 2*400 /3.5
t^2 = 228.57
t = 15.1 s.
Then, For Honda
t^2 = 2*350 /3 {Because he is already 50m ahead.}
t^2 = 233.33
t = 15.2 s
So, Porsche wins.
here we go. acceleration is the second order derivative of distance. is we’re gonne take the integrals(opposite) of these two accelerations two time, we will have the distance as a function of time. we will have
(Porsche) 3.5 m/s^2 (acceleration) => 3.5t (velocity) => (3.5t^2)/2 (distance)
(Honda) 3 m/s^2 (acceleration) => 3t (velocity) => 3/2 t^2 (distance)
Now, let’s find what time will the Porsche be in 400m away from the start. Let’s equate (3.5t^2)/2 to 400. We have t = 15s. That is, at 15 second the Porsche will be there (400m from the start). The question is where will Honda be at this time?
Let’s plug in the time to get the distance.
3/2 t^2 => 3/2 (15)^2 = 337.5
Since Honda gets ahead with 50 m distance, we should add 50m. So we have 387.5 m which is less than the Porsche’s.
And the winner is the PORSCHE….
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