Newton's 2nd Law Based Question

Question

A car with a mass m = 1280 kg is moving at a speed s = 25.9 km/h and needs to stop in a distance d = 30.5 m.

a) Write an expression for the magnitude of the net force on the car as it is stopping in terms of the symbols given in the problem statement.

Wouldn't it be |ΣF| = m * s?

b) What is the magnitude of the net force on the car as it is stopping, in N?

Answer 1

∫adt=v(t)=at+C (a is constant). Since v(0)=25.9 km/hr), v(t)=at+25.9.

vdt=x(t)=1/2at²+25.9t+C. Choose x(0)=0 thus C=0 and x(t)=1/2at²+25.9t

Choose v(T)=0 thus a=-25.9/T. Substitute this and solve x(T)=30.5m for T and a ... the Force will be 1280a.