On a horizontal, linear track lies a cart that has a fan attached to it. The mass of the cart plus fan is 364 g. The cart is positioned at one end of the track, and the fan is turned on. Starting from rest, the cart takes 4.49 s to travel a distance of 1.43 m. Now, mass is then added to the cart until the total mass of the cart-fan combination is 789 g, and the experiment is repeated. How long does it take for the cart, starting from rest, to travel 1.43 m? Assume that the cart travels with constant acceleration and ignore the effects due to friction.

6.32 s.

Explanation:

Given:

Mass of cart = 364 g

= 0.364 kg

Mass of cart with added mass = 789 g

= 0.789 kg.

Using equations of motion;

S = ut + 1/2 * at^2

S = a * t^2/2

1.43 = (a * 4.29^2)/2

= 0.155 m/s^2

F = m * a

= 0.364 * 0.155

= 0.0564 N

Acceleration, a2 of the new mass combination = F/m2

= 0.0564/0.789

= 0.0715 m/s^2

Calculating the new time, t2;

S = a * t2^2/2

1.43 = (0.0715 * t2^2)/2

t2^2 = 40

t2 = sqrt(40)

= 6.32 s.

= 0.155 m/s^2

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