An 800 kg car is moving at 32 m/s. What magnitude force is needed to bring that car to a stop in 30 seconds?

Kinematic relationship to get acceleration:

vf2 - vi2 = 2ax

vf = final speed = 0 m/s (comes to a full stop)

vi = initial speed = 32.0 m/s

x = distance over which the accelerating force acts to bring about a full stop = 30.0 m

a = acceleration

a = - vi2 / (2x) = - (32.0 m/s) 2 / [2 (30.0 m) ] = - 17.06 m/s2

The negative sign indicates it is a deceleration.

Newton's 2nd law:

F = ma = (800 kg) (-17.06 m/s2) = - 13648 N

The negative sign indicates the force is opposing the direction of motion. The magnitude of the force is

|F| = 13648 N