The 2-mg car is being towed by a winch. if the winch exerts a force of t=100(s+1)n on the cable, where s is the displacement of the car in meters, determine the speed of the car when s=10m, starting from rest. neglect rolling resistance of the car.

The speed of the car = 3.32 m/s

Explanation:

Speed: This can be defined as the rate of change of distance. The S.I unit of speed is m/s.

Note: From the question, The force acting on the car through the winch = The tension on the cable.

F = T = ma Equation 1

Where F = Force on the car, T = tension on the cable, m = mass of the car, a = acceleration of the car.

Where T = 100(s+1) N,

100(s+1) = ma Equation 2

making a the subject of equation 2

a = 100(s+1)/m Equation 3.

When s = 10 m, m = 2 Mg = 2×10³ kg = 2000 kg

a = 100(10+1)/2000

a = 0.55 m/s²

Using

v² = u²+2as Equation 4

Where a = 0.55 m/s², s = 10 m, u = 0 m/s

Substituting into equation 4

v² = 0² + 2(0.55)(10)

v² = 11

v = √11

v = 3.316

v ≈ 3.32 m/s.

Thus the speed of the car = 3.32 m/s