A cart on an air track is moving at 0.5m/s when the air issuddenly turned off. THe cart comes to rest in 1m. The experimentis repeated with the cart moving at 1 m/s when the air is turnedoff. How far does the cart travel before coming to rest?
a) 1 m
b) 2 m
c) 3 m
d) 4 m

D = 4 m

Explanation:

Speed of cart in air track v₁ = 0.5 m/s

Speed of cart moved when air is turned off v₂= 1 m/s

The distance travelled by the cart is d₁ = 1 m

Work done (W) = F x d

Work done is equal to the kinetic energy

F x d = 1/2mv²

velocity is directly proportional to distance

therefore,

v₁²/ v₂²  = d₁ / d₂

d₂ = d₁v₂² / v₁²

= 1 m x (1 m /s)² / (0.5 m/s)²

= 4 m