The position of an object moving along x-axis is given by x = a + bt2, where a = 8.5 m and b = 2.5 m s-2 and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

Question

The position of an object moving along x-axis is given by x = a + bt2, where a = 8.5 m and b = 2.5 m s-2 and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is (A) 5 m s-1 (B) 10 m s-1 (C) 15 m s-1 (D) 20 m s-1

Tardigrade Admin · Accepted Answer

Average velocity, barv=((x)t=4-(x)t=2/4-2) barv=((a+b(4)2)-(a+b(2)2)/4-2) =((a+16b)-(a+4b)/4-2)=6b =6(2.5)m s-1=15 m s-1

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

$5 m s^{- 1}$

$10 m s^{- 1}$

$15 m s^{- 1}$

$20 m s^{- 1}$

Average velocity, $\overset{v}{ˉ} = \frac{( x ) _{t = 4} - ( x ) _{t = 2}}{4 - 2}$
$\overset{v}{ˉ} = \frac{( a + b ( 4 ) ^{2} ) - ( a + b ( 2 ) ^{2} )}{4 - 2}$
$= \frac{( a + 16 b ) - ( a + 4 b )}{4 - 2} = 6 b$
$= 6 (2.5) m s^{- 1} = 15 m s^{- 1}$

Q. The position of an object moving along x-axis is given by x=a+bt2, where a=8.5m and b=2.5ms−2 and t is measured in seconds. The average velocity of the object between t=2s and t=4s is

5ms−1

10ms−1

15ms−1

20ms−1