Final answer:
The speed of the cart can be found by rearranging the formula for centripetal force to solve for velocity. By plugging in the given values into the rearranged formula, the calculated speed of the toy cart is 3.74 m/s.
Step-by-step explanation:
To calculate the speed of the toy cart, we need to use the formula for centripetal force F = m × v^2 / r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.
Given that the centripetal force is 40 N, the mass of the cart (m) is 2.0 kg, and the radius (r) of the circle, which is the length of the string, is 0.70 m, we can rearrange the formula to solve for v (velocity): v = √(F × r / m).
Substituting the given values:
v = √(40 N × 0.70 m / 2.0 kg) = √(14) m/s = 3.74 m/s