A car moves fast. The driver sees a stopped line of traffic ahead and brakes hard.
The one question that matters: how much road does the car need?
The car's kinetic energy answers it exactly.
Well, count the store that braking must remove. A 1000 kg car at 14 m/s carries ½ × 1000 × (14 × 14) of kinetic energy: 98000 J.
The brakes supply a steady 7000 N of force against the motion, so each meter of road removes 7000 J of that store.
The road needed is the store divided by the per-meter removal: d = 98000 / 7000 = 14, so the car stops in 14 m.
A 1000 kg car travels at 14 m/s. Its brakes supply a steady 7000 N of force against the motion. Calculate the stopping distance.
Write down the values:
m = 1000 kg, v_i = 14 m/s, F = 7000 N, d = ?
Write down the equation:
W_net = Fd
The kinetic energy to remove: (0.5 × 1000) × (14 × 14), which is 98000 J.
Substitute in the values, and calculate:
d = 98000 / 7000 = 14
The stopping distance is 14 m.
A crate slides across a floor. Friction, a steady 40 N, is the only horizontal force on it. The crate's kinetic energy falls by 100 J. Enter the distance it slid in m.
To find a force instead, divide the energy change by the distance it acted over.
A 3 kg cart speeds up from 2 m/s to 6 m/s along 3 m of straight track. Enter the net force on it in N.
On a wet day the same car's brakes can only supply 3500 N. Calculate the new stopping distance from 14 m/s.
Write down the values:
m = 1000 kg, v_i = 14 m/s, F = 3500 N, d = ?
Write down the equation:
W_net = Fd
The store to remove is the same 98000 J.
Substitute in the values, and calculate:
d = 98000 / 3500 = 28
The wet-day stopping distance is 28 m: half the force needs double the road.
Signs stay honest: a falling kinetic energy means negative net work, a net force against the motion. The sizes still divide the same way.
A 0.16 kg hockey puck leaves a stick with 8 J of kinetic energy. Ice friction, a steady 0.4 N, slows it until it stops. Enter the distance it slides in m.
An 800 kg car travels at 12 m/s when the driver brakes. The car must stop within 24 m. Enter the steady braking force that stops it in exactly that distance, in N.
A skater coasts across rough pavement. Friction on her wheels is a steady 36 N, and her kinetic energy falls by 1260 J before she rolls onto smooth concrete. Enter the distance she covered on the rough stretch in m.
A rider and bike together have a mass of 75 kg. Along 30 m of flat road, their speed rises from 4 m/s to 8 m/s. Enter the net force on them over that stretch in N.