Question

7. The position of a particle moving along x-axis at
a time t is x = (1+2t+3t)m. Its velocity at t= 4sec
is
ms
a) 26
b) 24
c) 15
d) 34​

Answer 1

Answer:

b 24

Explanation:

x=(1+2t+3t)m

x=t(1×2×3)

x=t(6)

t=4sec

x=4×6

x=24ms

Answer 2

CORRECT QUESTION

The position of a particle moving along x axis at a time t is x = (1+2t+3t^2)m. Its velocity at t= 4 sec is m/s

a) 26

b) 24

c) 15

d) 34

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Velocity\:of\:particle=26\:m/s}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given :}}} \\ \tt: \implies x = (1 + 2t + 3t^{2} )m \\ \\ \tt: \implies Time = 4 \: sec \\ \\ \red{\underline{\bold{To \: Find:}}} \\ \tt: \implies Velocity \: after \: 4 \: sec( v_{t = 4}) =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies x = 1 + 2t + 3 {t}^{2} \\ \\ \tt: \implies \frac{dx}{dt} = 1 + 2t + {3t}^{2} \\ \\ \tt: \implies v = 2 + 3 \times 2 \times t \\ \\ \tt: \implies v = 2 + 6t \\ \\ \tt: \implies v = 2 + 6 \times 4 \\ \\ \tt: \implies v = 2 + 24 \\ \\ \green{\tt: \implies v = 26 \: m/s} \\ \\ \green{\tt \therefore Velocity \: of \: particle \: after \: 4 \: sec \: is \: 26 \: m/s}$