Question

A car covers 72 kilometers in the first hour of its journey. In the next hour, it covers 90 kilometers. What is the amount of work done by the car? The total mass of the car, including its passengers, is 2. 5 Ă— 103 kilograms. A. 2. 8 Ă— 105 joules B. 4. 0 Ă— 105 joules C. 5. 1 Ă— 105 joules D. 2. 8 Ă— 106 joules E. 2. 8 Ă— 107 joules.

Answer 1

The work done by the car at the given mass and speed is $3.1 \times 10^5 \ J$

The given parameters;

• First distance traveled by the car, s = 72 km
• Second distance traveled, = 90 km
• Total time of motion, t = 2 hours
• Total mass = 2.5 x 10³ kg

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;

$a = \frac{\Delta v}{\Delta t} \\\\a = \frac{v- u}{t_2 - t_1}$

the initial time of motion, t₁ = 1 hour = 3600 s

the second time of motion, t₂ = 1 hour + 1 hour = 2 hours = 7200 s

$a = \frac{25-20}{7200 - 3600} \\\\a = 0.00138 \ m/s^2$

The force exerted by the car is calculated as follows;

$F = ma\\\\F = (2.5 \times 10^3) \times 0.00138 \\\\F = 3.45 \ N$

The work done by the car is calculated as follows;

$W = F\times s$

where;

• s is the displacement of the car

$s = (72 - 0) \ k m \ + \ (90 - 72) \ km\\\\s = 90 \ km = 90,000 \ m$

$W = 3.45 \times 90,000 \\\\W = 3.1 \times 10^5 \ J$

Thus, the work done by the car at the given mass and speed is $3.1 \times 10^5 \ J$.

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