What was the initial speed of this cart?

Question

A 10.8 kg runaway grocery cart runs into a spring with spring constant 250 N/m and compresses it by 50 cm. What was the speed of the cart just before it hit the spring?

Answer 1

Kinetic energy formula (K.E)= 0.5 * M* V^2, where M = mass of trolley (10.8 kg) and V is yet to be found.

Elastic potential energy (E.P.E)of the spring = 0.5 *k * x^2, where k is your spring constant and x would be the extension or compression in meters.

The E.P.E calculated from the given figures is 31.25 J

therefore K.E = 31.25 J = 0.5 * M* V^2.

Substituting M, gives V^2 = 5.787

Taking the square root, V = 2.41 m/s and thats the velocity of the your cart just before it hits the spring.