Parts which I am not sure about are in bold.
(a) A car of mass 1000 kg is initially at rest. It moves along a straight road for 20 s and then comes to rest again. The speed-time graph for the movement is:
(i) What is the total distance travelled?
(ii) What resultant force acts on the car during the part of the motion represented by CD?
(iii) What is the momentum of the car when it has reached its maximum speed? Use this momentum value to find the constant resultant accelerating force.
(iv) During the part of the motion represented by OB on the graph, the constant resultant force found in (iii) is acting on the moving car although it is moving through air. Sketch a graph to show how the driving force would have to vary with time to produce this constant acceleration. Explain the shape of your graph.
(b) If, when travelling at this maximum speed, the 1000 kg car had struck and remained attached to a stationary vehicle of mass 1500 kg, with what speed would the interlocked vehicles have travelled immediately after collision?
Calculate the kinetic energy of the car just prior to this collision and the kinetic energy of the interlocked vehicles just afterwards. Common upon the values obtained.
Explain how certain design features in a modern car help to protect the driver of a car in such a collision.
2. The attempt at a solution
(a) (i) Total distance = 250 m.
(ii) F = m * (v / t) = 1000 * (20 / 5) = 4000 N
(iii) p = mv = 1000 * 20 = 20 000 kg / ms
F = p / t = 20 000 / 10 = 2000 N
(iv) Shouldn't the graph be a linear graph just a horizontal line? On the given graph we have velocity / time and that means that the acceleration is constant (velocity is increasing). Because of constant velocity, the driving force F = ma is constant as well (m and a don't change). So in that case I would draw the graph a horizontal line. Is this logic right?
(b) 20 * 1000 = v (1000 + 1500) -> v = 8 m / s
KE = 1/2 mv2 = 0.5 * 1000 * 202 = 200 000 J
KE = 0.5 * 2500 * 82 = 80 000 J
The car had 200 kJ before and the combined KE is 80 kJ. So we can conclude that there was a serious accident and 120 kJ have transformed into sound and head.
Seatbelts, airbags, bumpers? Or the whole car is made out of a better material so when there is an collision the car doesn't deform much and the KE doesn't transform into heat and sound?