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 instantaneous velocity of the object at t = 2 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 instantaneous velocity of the object at t = 2 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

Here, x = a + bt2 Where, a = 8.5 m and b = 2.5 m s-2 Velocity, v=(dx/dt)=(d/dt)(a+bt2)=2bt At t=2 s, v = 2(2.5 m s-2)(2 s) = 10 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 instantaneous velocity of the object at $t = 2 s$ is

$5 m s^{- 1}$

$10 m s^{- 1}$

$15 m s^{- 1}$

$20 m s^{- 1}$

Here, $x = a + b t^{2}$
Where, $a = 8.5 m$ and $b = 2.5 m s^{- 2}$
Velocity, $v = \frac{d x}{d t} = \frac{d}{d t} (a + b t^{2}) = 2 b t$
At $t = 2 s$ ,
$v = 2 (2.5 m s^{- 2}) (2 s) = 10 m s^{- 1}$

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 instantaneous velocity of the object at t=2s is

5ms−1

10ms−1

15ms−1

20ms−1