A constant force is exerted on a cart that is initially at rest on an air track. Friction between the cart and the track is negligible. The force acts for a short time interval and gives the cart a certain final speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval

BLUE: four times as long as

YELLOW: twice as long as

PINK: equal to

PURPLE: half as long as

GREEN: a quarter of