Question

A 1,300 kg car is driving up a638.4 meters mountain. If itwill take 3.362 minutes to getto the top of the mountain, thecar's power (in horsepower) is:

Answer 1

Given that mass of the car, m= 1300 kg and displacement,x = 638.4 m and time taken to reach the top of the mountain, t = 3.362 minutes = 3.362 X 60 = 201.72 s

The velocity will be,

`\begin{gathered} v=(x)/(t) \\ =\text{ }(638.4)/(201.72) \\ =3.16\text{ m/s} \end{gathered}`

The acceleration will be

`\begin{gathered} a=(v)/(t) \\ =(3.16)/(201.72) \\ =0.015m/s^2 \end{gathered}`

As initial velocity is zero.

Also, the force will be

`\begin{gathered} F=ma \\ =1300*0.015 \\ =\text{ 19.5 N} \end{gathered}`

Thus Power will be,

`\begin{gathered} P=F* v \\ =19.5*3.16\text{ } \\ =61.62\text{ W} \end{gathered}`

Power value should be converted from W to hp as mentioned in the question.

`\begin{gathered} P=\text{ }\frac{\text{61.62}}{746} \\ =0.08\text{ hp} \end{gathered}`