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A car weighing $1200 kg$ is uniformly accelerated from rest and covers a distance of $40 m$ in $5$ seconds. Calculate the work the car engine had to do during this time.

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146.4 kJ

153.6 kJ

98.6 kJ

76.8 kJ

answer is B.

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Detailed Solution

A car weighing

1200 kg

is uniformly accelerated from rest and covers a distance of

40 m

5

seconds. The work the car engine had to do during this time is

153.6 kJ

.
Given:
mass,

m = 1200 kg

distance,

s = 40 m

time,

t = 5 s

initial velocity,

u = 0

[as car starts from the rest]
Using second equation of motion

s = ut + \frac{1}{2} a t^{2}

\Rightarrow

= 0 \times t + \frac{1}{2} a t^{2}

\Rightarrow

s = \frac{1}{2} a t^{2}

\Rightarrow

a = \frac{2 s}{t^{2}}

\Rightarrow

= \frac{2 \times 40}{(5)^{2}}

\Rightarrow

a = \frac{80}{25} m / s^{2}

∴

Work done

= F . s

\Rightarrow

= ma \times s

[as

F = ma

]

\Rightarrow

= 1200 \times \frac{80}{25} \times 40

\Rightarrow

= 153600

\Rightarrow

= 153.6 kJ

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