Question

Try making all three graphs for the following scenario:
1. John starts out north of home. At time zero he’s driving a cement
mixer south very fast at a constant speed.
2. He accidentally runs over an innocent cat crossing the road, so he slows to a stop to check on the poor cat.
3. He pauses for a while until he determines the cat is squashed flat and deader than a doornail.
4. Fleeing the scene of the crime, John takes off again in the same direction, speeding up quickly.
5. When his conscience gets the better of him, he slows, turns around, and returns to the crash site.

Answer 1

Let the speed of the cement mixer is u, distance covered is x, time t and acceleration be a.

so,

a) $x_1=u\times t$

AB part representing this part.

b) Let the acceleration is a, so

$v=u-at$

$0=u-at$

$u=at$

$x_2=ut-\dfrac{at^2}{2}$

$x_2=at^2-\dfrac{at^2}{2}=\dfrac{at^2}{2}$

BC part of the curve representing this part.

c)

Truck is paused for some time, so $x_3=0t+x_1+x_2=x_1+x_2$

CD part representing this part.

d)

Now, truck is speeding up with certain acceleration.

$x_4=\dfrac{a_1t^2}{2}$

DE part representing this part.

5) After the crash $x_5 =x_1+x_2+x_3+x_4$

EF part representing this part.