Question

Q15 A cyclist along with the machine weighs 80 kg .Starting from rest, he picks up a velocity of 15 m/s over a distance of 30 m . The power developed by the cyclist in 4 s is :

Answer 1

Answer

Power developed = 2250 W

Given

A cyclist along with the machine weighs 80 kg .Starting from rest, he picks up a velocity of 15 m/s over a distance of 30 m

To Find

Power developed by the cyclist in 4 s

Concept Used

3rd equation of motion

→ v² - u² = 2as

where ,

v denotes final velocity

u denotes initial velocity

a denotes acceleration

s denotes distance

_________________________

Newton's Second Law of motion

→ F = ma

where ,

F denotes force

m denotes mass of object

a denotes acceleration

_________________________

Work done

→ W = Fs

where ,

W denotes work done

F denotes force applied

s denotes distance

→ SI unit of Work is Joule

_________________________

Power developed

→ P = W/t

where ,

P denotes power developed

W denotes work done

t denotes time

→ SI unit of Power is Watt

_________________________

Solution

Mass , m = 80 kg

Initial velocity , u = 0 m/s

Final velocity , v = 15 m/s

Distance , s = 30 m

Acceleration , a = ? m/s²

Apply 3rd equation of motion ,

⇒ v² - u² = 2as

⇒ (15)² - (0)² = 2a(30)

⇒ 225 - 0 = 60a

⇒ 60a = 225

⇒ a = 3.75 m/s²

Apply Newton's Second Law ,

⇒ F = ma

⇒ F = (80)(3.75)

⇒ F = 300 N

Apply formula for work done ,

⇒ W = Fs

⇒ W = (300)(30)

⇒ W = 9000 J

Now , we need to find power developed by the cyclist in 4 s ,

$\to\ \bf P=\dfrac{W}{t}\\\\\to\ \rm P=\dfrac{9000}{4}\\\\\to\ \bf P=2250\ W$

So , power developed = 2250 W