Question

Bob is driving at 25.5 m/s when a deer steps into the road 52 m ahead of him. Assuming Bob immediately hits the

brakes and has a maximum braking acceleration of 7.2 m/s², will he be able to stop in time or will he hit the deer?
How many significant figures should the answer to this problem have?

Answer 1

Bob will be able to stop in time.

I think the final answer should be reported to two significant figures.

Step-by-step explanation:

First, it is necessary to calculate the time (in s) it takes ol' Bob to stop his vehicle. Use kinematic equation #1 and the given data to determine the time. For this problem, let

`V_i=25.5(m)/(s)\\V_f=0.0(m)/(s)\\a=-7.2(m)/(s^2)`

Acceleration is a negative value because it opposes the current motion of the vehicle.

So,

`V_f=V_i+at\\0.0(m)/(s)=25.5(m)/(s)+(-7.2(m)/(s^2))t\\-25.5(m)/(s)=(-7.2(m)/(s^2))t\\3.5s=t`

Next, use kinematic equation #2 and the calculated time to solve for Δx:

`\Delta x=((V_i+V_f)/(2))t\\\Delta x=((25.5(m)/(s)+0.0(m)/(s))/(2))(3.5s)\\\Delta x=(12.75(m)/(s))(3.5s)\\\Delta x=45.2m`

45.2m < 52m, so Bob and our crepuscular ungulate will not bump into each other.

I would say that the final answer should have two significant figures because the value for acceleration is given to two significant figures. The rules for significant figures state that when multiplying or dividing, the number of significant figures in the answer is determined by the value with the lowest number of significant figures. So, the value for time can only be recorded as having two significant figures. Since time is used as a multiplier to determine the distance traveled, the final answer should also be reported to two significant figures. I think.