Question

The position of an object moving along x-axis is given by x= a+bt^2 , where a= 8.5m and b = 2.5 ms^-2 and t is measured in seconds. What is the average velocity between t= 2s and t=4s.​

Answer 1

Solution

Given :-

• Position of an object is, x = a + bt² , moving alone x-axis .
• Value of a = 8.5 m , b = 2.5 m

Find :-

• Average velocity between t = 2s and, t = 4s

Explantion

Position of object ,

==> x = a + bt²___________(1)

Now, keep value of a & b,

Where,

• a = 8.5
• b = 2.5

==> x = 8.5 + 2.5t²__________(2)

Now, we calculate position of object at the point t = 2s and t = 4s

First, when

• t = 2s

==> x' = 8.5 + 2.5 × (2)²

==> x' = 8.5 + 2.5 × 4

==> x' = 8.5 + 10.0

==> x' = 18.5

Now, when

• t = 4s

==> x" = 8.5 + 2.5 × 4²

==> x" = 8.5 + 40.0

==> x" = 48.5

Now, calculate displacement

★Displacement = last position of object - first position of object.

So,

==> Displacement (s) = x" - x'

==> Displacement (s) = 48.5 - 18.5

==> Displacement (s) = 30 m.

Now, calculate time taken by object , covert first position to second position.

==> Time taken (t) = 4s - 2s = 2s .

According to question, We calculate here, average velocity.

Formula

$\boxed{\tt{\red{\:Average_{velocity}\:=\:\dfrac{Displacement}{Taken\:time}}}}$

So, now keep value,

==> Average velocity = 30/2

==> Average velocity = 15 m/s

Hence

• Average velocity of object will be = 15 m/s

______________________

Answer 2

15 m s

−1

Position is given as x=a+bt

2

=8.5+2.5t

2

Position at t=2 s, x

2

=8.5+2.5(2)

2

=18.5 m

Position at t=4 s, x

1

=8.5+2.5(4)

2

=48.5 m

Displacement S=x

2

−x

1

=48.5−18.5=30 m

Time taken t=4−2=2 s

Average velocity V

avg

=

t

S

=

2

30

=15 m/s