Answer to Question #244474 in Physics for Kimberly

Question

2.

A) The distance 𝑺 moved by an object in time 𝒕 may be given by the expression 𝑺 = 𝟏/ 𝟐

𝒂𝒕²

Where 𝒂 is the acceleration of the object.

State two conditions for this expression to apply to the motion of an object.

B) A car travelling along a straight road at a speed 𝒗. A hazard suddenly appears in front of the car. In the time interval between the hazard appearing and the brakes on the car coming into operation, the car moves forward a distance of 29.3m. with the brakes applied, the front wheels of the car leave skid marks on the road that are 12.8m. It is estimated that, during the skid, the magnitude of the decoration of the car is 0.85𝑔, where 𝑔 is the acceleration of free fall.

Determine

(i) The speed 𝑣 of the car before the brakes are applied,

(ii) The time interval between the hazard appearing and the brakes being applied .

(iii) The legal speed limit on the road is 60kmph. Use both your answers in (B) to comment on the standard of the driving of the car.

Answer 1

A) When the initial coordinate is 0 and the initial velocity is 0.

B) (i) The speed is

$$v=\sqrt{2gd}=14.6\text{ m/s}.$$

This is equivalent to 52.6 km/h.

(ii) The time is

$$t=\frac dv=2\text{ s}.$$

(iii) The driver did not break rules.