Atow truck is pulling a car out of a ditch by means of a steel cable (y = 2.0 x 1011 n/m2) that is 9.55 m long and has a radius of 0.437 cm. when the car just begins to move, the tension in the cable is 803 n. how much has the cable stretched?

If you know the real modulus of the cable (Y), the length, and the area (based on the radius), you can compute the spring constant, k = AE/L. Then, if you know the force used, you can compute the displacement, using F = kd, or d = F / k = FL/(AE). Our answer should work out to units of length. So, 
d = 803 N * 9.06 m / [pi*(0.574 cm)^2 * 2.0 x 10^11 N/m^2] 
d = 3.5 x 10^-8 Nm^3 / (cm^2 * N) 
d = 3.5 x 10^-8 m^3 / cm^2 * (100 cm / 1 m)^2 
d = 3.5 x 10^-4 m

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

    5.5 n======    assuming that      we have      m = 0.145 kg    a = 38 m/s²therefore    5.51 n, but two significant figures.final answer: 5.5 n