The motion of a particle is described by the equation x = at + bt2, where a = 15 cm s-1 and b = 3 cm s-2. Its instantaneous velocity at t = 3 s will be

Question

The motion of a particle is described by the equation x = at + bt2, where a = 15 cm s-1 and b = 3 cm s-2. Its instantaneous velocity at t = 3 s will be (A) 33 cm s-1 (B) 18 cm s-1 (C) 16 cm s-1 (D) 32 cm s-1

Tardigrade Admin · Accepted Answer

Here, x = at + bt2 where a = 15 cm s-1, b = 3 cm s-2 Velocity, v=(dx/dt)=(d/dt)(a+bt2)=a+2bt At t = 3 s, v = 15+ 2 × 3 × 3 = 33 cm s-1

Q. The motion of a particle is described by the equation $x = a t + b t^{2}$ , where $a = 15 c m s^{- 1}$ and $b = 3 c m s^{- 2}$ . Its instantaneous velocity at $t = 3 s$ will be

$33 c m s^{- 1}$

$18 c m s^{- 1}$

$16 c m s^{- 1}$

$32 c m s^{- 1}$

Here, $x = a t + b t^{2}$
where $a = 15 c m s^{- 1}$ , $b = 3 c m s^{- 2}$
Velocity, $v = \frac{d x}{d t} = \frac{d}{d t} (a + b t^{2}) = a + 2 b t$
At $t = 3 s$ , $v = 15 + 2 \times 3 \times 3$
$= 33 c m s^{- 1}$

Q. The motion of a particle is described by the equation x=at+bt2, where a=15cms−1 and b=3cms−2. Its instantaneous velocity at t=3s will be

33cms−1

18cms−1

16cms−1

32cms−1