Question

A car covers 90 km in 60 min, and a truck covers 54 km in the same period of time. The linear momentum of the truck is $15\times {10}^3$ kg m/s. The mass of the car is 500 kg.

The ratio of the kinetic energy of the car to the kinetic energy of the truck is:

[1 mark]

• A. 25:18
• B. 5:9
• C. 18:25
• D. 9:5

Answer 1

The correct option is A 25:18

Given,
Speed of the car = 90 km/hr = 25 m/s
Speed of the truck = 54 km/hr = 15 m/s
Mass of the car = 500 kg
Linear momentum of the truck = 15,000 kg m/s

For the truck:
Kinetic energy,
K.E. = $\frac{1}{2}m{v}^2$
$\Rightarrow K.E.=\frac{1}{2}\times 1000\times {15}^2$
$\Rightarrow K.E.=1,12,500J$

For the car:
Kinetic energy,
K.E. = $\frac{1}{2}m{v}^2$
$\Rightarrow K.E.=\frac{1}{2}\times 500\times {25}^2$$\Rightarrow K.E.=1,56,250J$

The ratio of the kinetic energy of the car to that of the truck $=\frac{K.E.c^{}}{K.E.t^{}}=\frac{1,56,250}{1,12,500}=\frac{25}{18}$

Where $K.E.c^{}$ = Kinetic energy of the car
and $K.E.t^{}$ = Kinetic energy of the truck