Question

the mass of a locomotive at rest is 10^5 grams. the locomotive started to move from a shunting point and accelerated at 1m/s^2 for 50 seconds. Find the work done by the locomotive. find the power generated by the locomotive

Answer 1

to find :

• the work done by the locomotive
• the power generated by the locomotive

given :

• mass of the locomotive, m = 10^5 g
• initial velocity , u = 0m/s
• acceleration, a = 1m/s^²
• time, t=  50 s

formula to be used:

• final velocity = u+at
• work = 1/2*m(v²-u²)
• power = work/time

solution :

acceleration = 1m/s²

time = 50

initial velocity = 0m/s

so, final velocity , v = u+at

$\longrightarrow \bold{v= 0+(1*50)}\\\longrightarrow \bold{v= 0+50}\\\longrightarrow\bold{\boxed{\bold{\red{v= 50m/s}}}}$

mass = 10^5 g

$\longrightarrow\bold{mass = 10^5}\\\longrightarrow\bold{mass = 1,00,000\: g}$

work = 1/2*m(v²-u²)

$\longrightarrow\bold{work = \frac{1}{2}*m(v^2-m^2)} \\\\\longrightarrow\bold{work = \frac{1}{2}*100000(50^2-0^2) }\\\\\longrightarrow\bold{work = \frac{1}{2}*100000(2500) }\\\\\longrightarrow\bold{work = 250000000*\frac{1}{2} }\\\\\longrightarrow\boxed{\bold{work=125000000 \:J}}$

power generated= work/time

$\longrightarrow\bold{power = 125000000/50}\\\longrightarrow\boxed{\bold{power=25000000 W}}$

hence,

$\longrightarrow\boxed{\bold{work\: done= 1.25*10^8\:J}}\\\longrightarrow\boxed{\bold{power = 2.5*10^7\: W}}$