<p>The nonlocal strain gradient and velocity gradient theories were applied to study sandwich nanoplates’ dynamic response to low-velocity impact. The impact force comes from the van der Waals contact forces between the impactor and nanoplate. Combining nonlocal velocity gradient and strain gradient theories add three scale parameters to the constitutive equations and produce more accurate results. The displacement equations were calculated using layer-wise first-order zig-zag theory. The governing equations were solved using the Ritz and fourth-order Runge–Kutta techniques. The dynamic responses of the contact force, reflected velocity, plate deflection, and impactor displacement were investigated using the numerical findings. The nonlocal parameters, nanoplate fiber orientation, and impactor material are all important components. A case comparison study verified the technique and outcomes, demonstrating great accuracy. Some nonlocal characteristics, such as the kinetic material length scale parameter, enhance the nanoplate softness, and cause the impactor to waste more energy on it, increasing the nanoplate deflection and decreasing the contact force. Increasing the kinetic length scale parameter by up to 300% results in a decrease in interaction force to 4% and an increase in deflection to 15%. Different impactor materials significantly alter impact dynamics. Impactors with higher Lennard-Jones force parameters interact with the nanoplate earlier. The silicon impactor with a Lennard-Jones attraction parameter three times greater than that of platinum, reaches the plate 0.0015 nanoseconds earlier. A high impactor density increases the nanoplate deflection and contact force. However, this occurrence lowers the impactor reflected velocity and displacement slope.</p>