Video Transcript
The graph shows the change in the
velocity of a car over time. The driver notices an obstacle at
time zero. They then react by applying the
brakes. The vehicle then decelerates and
eventually comes to a complete stop. What is the thinking distance of
the driver of the vehicle?
In this question, we are given a
velocity–time graph and we want to calculate the thinking distance of the driver of
the vehicle.
The thinking distance is the
distance traveled by the driver during the time it takes for them to react to the
obstacle. In other words, it’s the distance
traveled in the interval of time between the driver noticing the obstacle and
actually applying the brakes. Recall that the thinking distance
is given by the equation 𝑑 thinking equals 𝑢𝑡 reaction, where 𝑑 thinking is the
thinking distance, 𝑢 is the initial velocity, and 𝑡 reaction is the reaction
time.
Looking at the velocity–time graph,
we can see that the velocity at time zero is 15 meters per second. We can also see that this initial
velocity is maintained until 𝑡 equals three seconds, when the velocity begins to
decrease. The time 𝑡 equals three seconds
corresponds to the moment that the driver applies the brakes on the vehicle, causing
its velocity to slow down.
So, although the driver noticed the
obstacle at 𝑡 equals zero seconds, they didn’t react to the obstacle by applying
the brakes until three seconds later. And so three seconds is the value
of the driver’s reaction time.
If we now substitute in the values
of initial velocity and reaction time into the equation for thinking distance, we
find that the thinking distance is equal to 15 meters per second multiplied by three
seconds. Completing this calculation, we
find that the thinking distance is equal to 45 meters. And so we have arrived at the
correct answer. The thinking distance of the driver
of the vehicle is 45 meters.
