The initial speed of the cart is 1.3m/s.
The velocity of an object is the rate of change of its position with respect to a given time interval.
Given
Mass m of the cart = 12kg
Spring constant =290 N/m.
The compressed length of the spring = 10 cm.
The initial kinetic energy of the cart is given below.
K.E. = 1/2 m v2
v = initial velocity of the cart.
When the cart hits the spring, it is compressed by the cart. When the cart stops, due to the maximum compression, the kinetic energy of the cart will be zero. Hence its kinetic energy will be converted into elastic potential energy of the spring. This is given as,
U = 1/2 kx²
k = spring constant
x = compressed length of the spring.
This elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
U = 1/2 * 290*(0.80)² = 0.64.
U = 64J.
Elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
64 = (1/2) * 80 * v²
128 = 80 * v²
v² = 128/ 80
v² = 1.6
v = 1.26 ≅ 1.3
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