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Interactive Lab · Mechanics

Energy–Kinematics Explorer

Describe one trip down an incline in two languages—and verify that both predict the same final speed.

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t = 0.00 s
Cart moving down an inclineA cart at the top of an incline with live position and velocity vectors.
0.00 m along track0.00 m/s4.91 m/s²10.00 m track

Same event, two descriptions

Two routes to final speed

The cart reaches the bottom.

Kinematics
a=g(sin⁡θ−μkcos⁡θ),vf2=vi2+2aΔxa=g(\sin\theta-\mu_k\cos\theta),\qquad v_f^2=v_i^2+2a\Delta x

Friction is included in the acceleration through the normal force.

Energy
Ki+Ui+Wfriction=KfK_i+U_i+W_{\mathrm{friction}}=K_f

Friction transfers mechanical energy into thermal energy.