Question

You are driving on a highway at 20 m/s. Suddenly you see a deer step into the road, 110 m in front of you. Assume that your reaction time is 0.70 s and that your car brakes with constant accerleration.

A.)How far are you from the deer when you begin to apply the brakes?
B.)What accerleration will bring you to a rest right at the deer's posion.
C.) How long does it take you to stop?

Answer 1

You are driving on a highway at $20\,\mathrm{m/s}$. Suddenly you see a deer step into the road, $110\,\mathrm{m}$ in front of you. Assume that your reaction time is $0.70\,\mathrm{s}$ and that your car brakes with constant acceleration.

A.) How far are you from the deer when you begin to apply the brakes?

B.) What acceleration will bring you to a rest right at the deer's position.

C.) How long does it take you to stop?

Solution

A.) Before braking, you travel at $20\,\mathrm{m}$ per second for 0.7 seconds, making $14\,\mathrm{m}$.

The distance remaining to the deer is $110 - 14 = 96\,\mathrm{m}$.

B.) Now use that equation of motion which includes distance S, acceleration a and starting and end velocities, u and v.

$$v^2 - u^2 = 2aS$$

Final velocity $v = 0$

Start velocity $u = 20$

Distance $S = 96$

So

$$0 - (20^2) = 2*a*96 \rightarrow a = -\frac{25}{12} \sim -2.08\,\frac{\mathrm{m}}{\mathrm{s}^2}$$

C.) Time for stop = reaction time + deceleration time

$$t_d = \frac{u}{a} = \frac{20}{2.08} = 9.6\,\mathrm{s}$$

So $t = 9,6 + 0,7 = 10.3\,\mathrm{s}$.

Answer: $96\,\mathrm{m};\ -2.08\,\frac{\mathrm{m}}{\mathrm{s}^2};\ 10.3\,\mathrm{s}$.