Question

A large truck of mass 5000 kg is travelling at 5.0 m/s.
A motorbike has a mass of 200 kg. Both the truck and the motor bike have the same kinetic energy
What is the speed of the motorbike?
A 25 m/s
B 10 m/s
C 125m/s
D 2.5 m/s​

Answer 1

Answer:

A. 25m/s

Explanation:

kinetic energy of truck=kinetic energy of bike

1/2 ×5000× (5)^2 = 1/2 ×200× v^2

5000×25 =200 v^2

v^2 = (5000×25)/200

v^2 = 125000/200

v^2 = 625

v = ✓(625)

v = 25

Thus the speed of the bike is 25 m/s

Answer 2

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

${\Large{\mathcal \ Given \ :-}}$

• Mass of truck = 5000kg
• Velocity of truck = 5.0 m/s
• Mass of motorbike = 200 kg

${\Large{\mathcal \ To \ find \ :-}}$

• Velocity of motorbike

${\Large{\mathcal \ Solution \ :-}}$

${\tt{Let \ v \ be \ the \ velocity \ of \ motorbike}}$

${\boxed{\sf \star \ Kinetic \ energy = \frac{1}{2} m {v}^{2} }}$

Here

• m is mass
• v is velocity

${\sf{\Longrightarrow \ k.e \ of \ truck \ = \ \frac{1}{ \cancel2} \times \cancel{5000} \times 5 \times 5}}$

${\sf{\Longrightarrow \ k.e \ of \ truck \ = \ 2500 \times 5 \times 5}}$

${\sf{\Longrightarrow \ k.e \ of \ truck \ = \ 62500 J}}$

_______________

Since it is given that the kinetic energy of truck is equals to the kinetic energy of motorbike

${\sf{\Longrightarrow \ Kinetic \ energy \ of \ motorbike \ = \ \frac{1}{2} \times m \times {v}^{2} }}$

${\sf{\Longrightarrow \ 62500 = \frac{1}{\cancel2} \times \cancel{200} \times {v}^{2} }}$

${\sf{\Longrightarrow \ 62500 = 100 \times {v}^{2} }}$

${\sf{ \Longrightarrow \ {v}^{2} = \frac{62500}{100} }}$

${\sf{ \Longrightarrow \ {v}^{2} = 625}}$

${\sf{\Longrightarrow \ v = \sqrt{625} }}$

${\bold{\sf \Longrightarrow \ v= 25 \ m/s}}$

Hence option (a) is correct.

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