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The work done by the car at the given mass and speed is [tex]3.1 \times 10^5 \ J[/tex]
The given parameters;
The initial velocity of the car, u = 72 km/h = 20 m/s
The final velocity of the car, v = 90 km/h = 25 m/s
The acceleration of the car is calculated as follows;
[tex]a = \frac{\Delta v}{\Delta t} \\\\a = \frac{v- u}{t_2 - t_1} \\\\[/tex]
the initial time of motion, t₁ = 1 hour = 3600 s
the second time of motion, t₂ = 1 hour + 1 hour = 2 hours = 7200 s
[tex]a = \frac{25-20}{7200 - 3600} \\\\a = 0.00138 \ m/s^2[/tex]
The force exerted by the car is calculated as follows;
[tex]F = ma\\\\F = (2.5 \times 10^3) \times 0.00138 \\\\F = 3.45 \ N[/tex]
The work done by the car is calculated as follows;
[tex]W = F\times s[/tex]
where;
[tex]s = (72 - 0) \ k m \ + \ (90 - 72) \ km\\\\s = 90 \ km = 90,000 \ m[/tex]
[tex]W = 3.45 \times 90,000 \\\\W = 3.1 \times 10^5 \ J[/tex]
Thus, the work done by the car at the given mass and speed is [tex]3.1 \times 10^5 \ J[/tex].
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