Question

A car drives in a highway exceeding the seed limit with a constant seed of 160 km/h and passes a motion less police car. Emediately the police car commences the persue in the exact instant the first car passes the police car. The police car accelerates the vehicle at 3 m/s^2 constantly if it continues at thi rate; calculate the time it will spend to catch up with the civilian car and the distance it will take to do so.

Answer 1

Answer on Question #47492, Physics, Mechanics - Kinematics - Dynamics

A car drives in a highway exceeding the speed limit with a constant seed of $160~\mathrm{km/h}$ and passes a motion less police car. Immediately the police car commences the peruse in the exact instant the first car passes the police car. The police car accelerates the vehicle at $3~\mathrm{m/s^2}$ constantly if it continues at this rate; calculate the time it will spend to catch up with the civilian car and the distance it will take to do so.

Distance, traveled by the car:

$$S = v t$$

Police car should travel the same distance at the same time:

$$S = \frac{a t^{2}}{2}$$

We will get equation

$$v t = \frac{a t^{2}}{2} \Rightarrow t = \frac{2 v}{a} = 2 \cdot \frac{160~\mathrm{m}}{\frac{3.6~\mathrm{s}}{3~\mathrm{m}~\mathrm{s}^{2}}} \approx 29.6~\mathrm{s}$$

Traveled distance:

$$S = \frac{160~\mathrm{m}}{3.6~\mathrm{s}} \cdot 29.6~\mathrm{s} \approx 1316~\mathrm{m}$$

Answer: time to catch $t \approx 29.6~\mathrm{s}$

Traveled distance: $S \approx 1316~\mathrm{m}$

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