Question

A small coin, initially at rest, begins falling. If the clock starts when the coin begins to fall, what is the magnitude of the coin\'s displacement between t1 = 0.2212 s and t2 = 0.737 s?

Answer 1

The magnitude of the coin's displacement between times t1 = 0.2212 s and t2 = 0.737 s is 2.4183 meters. This was calculated using the formula for displacement in one-dimensional motion under gravity, given the initial velocity is zero.

Step-by-step explanation:

The question pertains to the displacement of a falling coin over a specific time interval. We are dealing with a physics problem that involves one-dimensional motion under gravity, also known as free-fall. Since the initial velocity (u) of the coin is zero, we can use the equation of motion for constant acceleration (gravity) to find the displacement (s):

s = ut + ½ at^2

Where:

• u = initial velocity (0 m/s, since the coin starts at rest)
• a = acceleration due to gravity (9.8 m/s2 on Earth)
• t = time

We are interested in the displacement between two times, t1 = 0.2212 s and t2 = 0.737 s.

To find the displacement at t1, we substitute the values into the equation:

s1 = 0 × 0.2212 + ½ × 9.8 × (0.2212)^2 = 0.2407 m

Now, let's find the displacement at t2:

s2 = 0 × 0.737 + ½ × 9.8 × (0.737)^2 = 2.659 m

The magnitude of the coin's displacement between t1 and t2 is simply the difference between s2 and s1:

|Displacement| = |s2 - s1| = |2.659 m - 0.2407 m| = 2.4183 m

Thus, the coin's displacement between the given times is 2.4183 meters.

Answer 2

As per question the coin is falling under gravity as there is no other force that has bee mentioned here.

so the equation of motion for a freely falling body is given as-
`s=ut-(1)/(2) gt^2`

here the initial velocity is zero as the coin was at rest.

hence we have
`s=(1)/(2) gt^2`

so now we have to calculate the displacement of the coin at various instants.

at t=0.2212 s,we have

`s=(1)/(2) 9.801*[0.2212]^2`

=0.2398m[upto four decimal digit

again when t=0.737 s

s=
`(1)/(2) *9.801*[0.737]^2`

=2.662m [upto three decimal digit] [ans]