The velocity-time relation of a particle starting from rest is given b

1.	The velocity-time relation of a particle starting from rest is given by v = kt where k = 2 m/s2. The distance travelled in 3 sec is(A) 9 m (B) 16 m (C) 27 m (D) 36 m
Answer» Correct Option is (A) 9 m Given, V = kt \(\because v = \frac{dx}{dt}\) \( \frac{dx}{dt} = kt\) \(\int\limits_0^x dx = \int\limits_ 0^3 kt \ dt\) \(x = k \left[\frac{t}{2}\right]_0^3\) \(x = k \left[\frac{9}{2}\right]\) \(x = 2 \times \frac{9}{2}\). x = 9 m Correct option is: (A) 9 m

The velocity-time relation of a particle starting from rest is given by v = kt where k = 2 m/s2. The distance travelled in 3 sec is(A) 9 m (B) 16 m (C) 27 m (D) 36 m

Answer»

Correct Option is (A) 9 m

Given,

V = kt

\(\because v = \frac{dx}{dt}\)

\( \frac{dx}{dt} = kt\)

\(\int\limits_0^x dx = \int\limits_ 0^3 kt \ dt\)

\(x = k \left[\frac{t}{2}\right]_0^3\)

\(x = k \left[\frac{9}{2}\right]\)

\(x = 2 \times \frac{9}{2}\).

x = 9 m

Correct option is: (A) 9 m