In: Physics
Q: A child is running at her maximum speed of 4.0 m/s to catch an ice-cream truck, which is stopped at the side of the road. When the child is 20 m from the truck, the ice-cream truck starts to accelerate away at a rate of 1.0 m/s2 . Does the child catch the truck? solve this problem algebraically and graphically.
Algebraic method :
Let the velocity of the child is v = 4.0 m/s. And the acceleration
of the ice cream truck is a = 1.0 m/s^2.
And as there is an initial gap d = 20 m, so, we have at time t, the
distance travelled by the child is
And similarly, the distance travelled by the ice cream truck
is
And the child will be able to catch the truck if at the time t the
child also cover the extra initial distance between the child and
the truck. So, the condition is
And so, we get
Now in the given case,
And so,
So, the time is imaginary. So, this implies that the child will
never be able to catch the truck.
Graphically :
We plot the two functions
And
on the same plot. And this implies
And the two plots implies that they will not intersect at any
finite time t. And so, we see that the child will not be able to
catch the truck.