Define watt. Express kilowatt in terms of joule per second. A 150 kg car engine develops 500 W for each kg. What force does it exert in moving the car at a speed of $20 m s^{- 1} ?$

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Solution

Step1: Definition of power.
Power is defined as the rate at which work is done upon an object. Power is a time-based quantity, which is related to how fast a job is done. The formula for power is mentioned below.
$P o w e r = W o r k / t i m e$
$P = W / t$
The SI unit of power is the watt. One watt of power is equal to one Joule of energy consumed in one second.
$1 W a t t = 1 J o u l s e / 1 s e c o n d$

Step 2: kilowatt in terms of joules per second.
As $1 W a t t = 1 J o u l s e / 1 s e c o n d$
Therefore, $1 k i l o w a t t = 1000 w a t t s = 1000 J / s e c$

Step3: Calculation of force.
$M a s s o f c a r = 150 k g$ (given)
$p o w e r f o r e a c h k g = 500 W$ (given)
$S p e e d = 20 m / s$ (given)
$T h e r e f o r e, t o t a l p o w e r d e v e l o p e d f o r 150 k g = 500 \times 150 = 75000 W$ .
$A s P = \frac{W}{T} = \frac{F . S}{T} = F . \frac{S}{T} = F . V (∵ V = \frac{S}{T}, W h e r e S i s d i s p l a c e m e n t)$
$∴ F o r c e = P o w e r / v e l o c i t y = 75000 / 20 = 3750 N$
Hence the total force exerted to move the car is 3750 Newton.

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Define watt. Express kilowatt in terms of joule per second. A 150 kg car engine develops 500 W for each kg. What force does it exert in moving the car at a speed of 20ms-1?

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