Calculate the time elapsed

Question

A car of mass 1800 kg moves from rest , if the power of the engine is constant and equals 75 horse after how many seconds does it speed get 17.5 m/s $$a)\; 5 $$ $$b)\; 10 $$ $$c)\; 2 $$ $$d)\; 7.5$$ My turn: $$P= F \times V , F = 3150 \,\mathrm{N}$$ $$F = m a , a = 1.75\,\mathrm{ m/s^2}$$ $$V = V0 + at , t =\frac{17.5}{1.75}= 10\, \mathrm{s}$$ But the correct answer is 5 s So what the mistake i have done ?

Answer 1

Your mistake is you assumed the acceleration is constant. The acceleration is proportional to the force, which is not constant.

Since the power $P$ is constant and since (as you know) $F = \frac PV,$ as $V$ increases (from $0$ to $17.5$) the force must decrease.

You are better off to ignore the force entirely. Instead, you can use other facts about power.

Work is related to power and time. Kinetic energy is related to work and also to velocity. This is a good opportunity to review all the formulas.

Answer 2

Note that the kinetic energie $E_{kin}$ gained by the acceleration is

• $E_{kin} = \frac{m}{2}v^2$

For this energy it holds

• $E_{kin} = Pt$

Note, that

• $1 \mbox{horse} = 735.49875 \frac{kg\cdot m^2}{s^3}$

Putting all this together you get $$E = Pt\Rightarrow t = \frac{E}{P}= \frac{mv^2}{2P} = \frac{1800\cdot 17.5^2}{2\cdot 75\cdot 735.49875}s \approx 5 s$$