Question

A marble begins at the zero mark on a 2-m stick (it is 2.0000 m so assume it is exactly 2 m) and moves at a steady 35 cm/s. A toy car starts at the same time the marble begins rolling at the 2.000 m mark of the stick. The car moves toward the marble starting from rest and accelerating at 0.40 m/s². Find how long it takes until they collide and at what cm mark on the 2-m stick they collide.Please also draw a picture.

Answer 1

The problem is related to one-dimensional motion. The given quantites in question are as follows:

The marble is moving with constant velocity (uniform motion) v = 0.35 m/s

Toy car start from rest and moving with constant accelartion a = 040 m/s²

Assume, at distance x from zero mark the marble collide with toy car. This is shown in figure below:

Considering the motion of marble:

Acceleration a = 0

velocity v = 0.35m/s

By applying equation of motion:

we get

Considering the motion of toy car :

Displacement = 2 - x

Initial velocity u = 0

Acceleration a = 0.40 m/s²

By applying equation of motion:

By solving equation 1 and 2 ,

Substituting t in equation 2 , we get

From above two equation , we get a quadratic equation as follows:

By solving, we get x= 0.8421 m and x = -1.4544 m

Since x will never be negative . we take x = 0.8421 m

So marble and toy car collide at x = 0.8421 m

Time taken to collide eachother is given by:

Time at which marble collide with toy car = 2.4 s

The mark on 2m stick they collide = 0.8421 m = 84.21 cm

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