A vehicle of mass m is driven by an engine of power P from rest. Find the minimum time it will take to acquire a speed
\(\frac{mv^2}{2p}\)
\(\frac{mv^2}{p}\)
\(\frac{mv}{p}\)
\(\frac{mv}{2p}\)
Explanation
Video Explanation
No video available
Post your Contribution
Discussions (18)
@myschool, the options fielded are not correct
It ought to be mv²/p.......
My concern is why the answer is mv²/p and not mv²/2p
If you solve it this way👇
Power, p=energy/time,=k.e/time
K.e=½mv²
Power,p=mv²/2t
(Make t the subject of the expression)
t=mv²/2p✓
But if I solve it in this other way👇
Power=force × velocity
Power, p= m•a•v
acceleration,a=v/t
Power,p=m•v•v/t
Power, p=mv²/t
(Make t the subject of the expression)
Then t=mv²/p as you picked as the answer.
Students will now be left in a dilemma as to which or what option to pick
This came as a controversy in one of jamb's questions
I think it is-A car of mass 800kg attains a speed of 25m/s in 20 secs. The power developed in the engine is
The answer you picked was different from that we solved
Your way seems valid and ours also valid
I am just confused
Should we turn it to power duality principle 😔
B is the correct 💯 answer here... I have come across such and here's why 👇
Power is the rate change of Energy with time also...
P = ∆E/∆t
But the K.E of the vehicle is ½mv² and equal to ∆E
Therefore ∆E = K.E where K.E is ½mv²
And that is the final K.E of the vehicle as it's initial is 0...
So now substituting ½mv² into Power since it is equal to ∆E👇
P = ½mv²/∆t
Making ∆t subject formula we have 👇
∆t = ½mv²/p
Power= force × velocity
Force= Mass × acceleration
acceleration = velocity /time
Force =mass× (velocity/time).....
Substituting acceleration with v/t
Power =(mass×velocity /time) ×velocity......Substituting F with mv/t
P=(mv/t) × v
P=MV²/t
Cross multiply
Pt=MV²
Divide both side by P to get t
t=MV²/p
I believe you have physics guru among you please find the correct answer to this question 🙏🙏🙏🙏
You guys power is Mass ×Velocity2 /2×time
That's the mix-up from all I've read. It's mv2/2t not mv2/t
