Question

A 1000.0 kg car is moving at 15 km/h. if a 2000.0 kg truck has 18 times the kinetic energy of the car, how fast is the truck moving?

Answer 1

45 km/h

Step-by-step explanation:

The kinetic energy of the car is given by:

`K=(1)/(2)mv^2`

where

m=1000.0 kg is the mass of the car

v=15 km/h is its speed

The kinetic energy of the truck is given by:

`K'=(1)/(2)MV^2`

where

M = 2000.0 kg is the mass of the truck

V is its unknown speed

We know that the truck has 18 times the kinetic energy of the car, therefore:

`K'=18 K`

Substituting and re-arranging, we can find V:

`(1)/(2)MV^2 = 18 \cdot (1)/(2)mv^2\\V=\sqrt{(18 mv^2)/(M)}=\sqrt{(18(1000.0 kg)(15 km/h)^2)/((2000.0 kg))}=45 km/h`

Answer 2

1)First calculate the kinetic energic of the car:

kinetic energy=
`(1)/(2) m.v^2`
m-mass of the car: 1000kg
v-velocity of the car: 15 km/h
kinetic energy of the car=
`(1)/(2) * 1000 *15 ^(2)`
= 112500 Joules

2) calculate the kinetic energic of the truck
kinetic energy=
`(1)/(2) m.v^2`
m-mass of the car: 2000kg
v-velocity of the car: unknown
kinetic energy of the truck= the kinetic energy of the car multiplied by 18= 112500 x 18= 2025000 joules

2025000=
`(1)/(2) * 2000 *v ^(2)`
2025= v^2
√2025 = 45

the velocity of the truck = 45 km/h